Question 1: Palette 1/275

JEE Mains 2026 MCQ

Which one of the following is not a measurable quantity?

A

Resistance

B

Voltage difference

C

Displacement current

D

Voltage

Question 2: Palette 2/275

JEE Mains 2026 MCQ

A Wheatstone bridge is initially at room temperature and all arms of the bridge have same value of resistances ($R_1 = R_2 = R_3 = R_4$). When $R_3$ resistance is heated to some temperature, its resistance value has gone up by 10%. The potential difference ($V_a - V_b$) (after $R_3$ is heated) is _________ V.

A

1.05

B

0.95

C

0

D

2

Question 3: Palette 3/275

JEE Mains 2026 MCQ

For the two cells having same EMF $E$ and internal resistance $r$, the current passing through the external resistor $6 \Omega$ is same when both the cells are connected either in parallel or in series. The value of internal resistance $r$ is $\_\_\_\_$ $\Omega$.

A

3

B

6

C

4

D

9

Question 4: Palette 4/275

JEE Mains 2026 MCQ

In the potentiometer, when the cell in the secondary circuit is shunted with $4 \Omega$ resistance, the balance is obtained at the length 120 cm of wire. Now when the same cell is shunted with $12 \Omega$ resistance, the balance is shifted to a length of 180 cm . The internal resistance of cell is $\_\_\_\_$ $\Omega$

A

4

B

12

C

6

D

3

Question 5: Palette 5/275

JEE Mains 2026 MCQ

The reading of the ammeter $(A)$ in steady state in the following circuit (assuming negligible internal resistance of the ammeter) is $\_\_\_\_$ A.

A

1/2

B

1

C

2

D

0

Question 6: Palette 6/275

JEE Mains 2026 MCQ

A moving coil galvanometer of resistance $100 \Omega$ shows a full scale deflection for a current of 1 mA . The value of resistance required to convert this galvanometer into an ammeter, showing full scale deflection for a current of 5 mA , is $\_\_\_\_$ $\Omega$

A

25

B

2.5

C

0.5

D

10

Question 7: Palette 7/275

JEE Mains 2026 MCQ

A regular hexagon is formed by six wires each of resistance $r \Omega$ and the corners are joined to the centre by wires of same resistance. If the current enters at one corner and leaves at the opposite corner, the equivalent resistance of the hexagon between the two opposite corners will be

A

$\frac{3}{5} r$

B

$\frac{4}{5} r$

C

$\frac{5}{8} r$

D

$\frac{3}{4} r$

Question 8: Palette 8/275

JEE Mains 2026 MCQ

Two resistors of $100 \Omega$ each are connected in series with a 9 V battery. A voltmeter of $400 \Omega$ resistance is connected to measure the voltage drop across one of the resistors. The voltmeter reading is $\_\_\_\_$ V.

A

3

B

2

C

4

D

4.5

Question 9: Palette 9/275

JEE Mains 2026 MCQ

Two resistors $2 \Omega$ and $3 \Omega$ are connected in the gaps of bridge as shown in figure. The null point is obtained with the contact of jockey at some point on wire $X Y$. When an unknown resistor is connected in parallel with $3 \Omega$ resistor, the null point is shifted by 22.5 cm toward $Y$. The resistance of unknown resistor is $\_\_\_\_$ $\Omega$.

A

3

B

1

C

4

D

2

Question 10: Palette 10/275

JEE Mains 2026 MCQ

To compare EMF of two cells using potentiometer the balancing lengths obtained are 200 cm and 150 cm . The least count of scale is 1 cm . The percentage error in the ratio of EMFs is $\_\_\_\_$

A

1.75

B

1.55

C

1.17

D

1.65

Question 11: Palette 11/275

JEE Mains 2026 MCQ

A wire of uniform resistance $\lambda \Omega / \mathrm{m}$ is bent into a circle of radius $r$ and another piece of wire with length $2 r$ is connected between points $A$ and $B(\mathrm{AOB})$ as shown in figure. The equivalent resistance between points $A$ and $B$ is $\_\_\_\_$ $\Omega$.

A

$(\pi+1) 2 r \lambda$

B

$\frac{6 \pi \lambda r}{3 \pi+16}$

C

$\frac{3 \pi \lambda r}{8}$

D

$2 \pi \lambda r$

Question 12: Palette 12/275

JEE Mains 2026 MCQ

An electric power line having total resistance of $2 \Omega$, delivers 1 kW of power at 250 V . The percentage efficiency of transmission line is $\_\_\_\_$ .

A

96.9

B

92.5

C

86.5

D

100

Question 13: Palette 13/275

JEE Mains 2026 MCQ

A meter bridge with two resistances $R_1$ and $R_2$ as shown in figure was balanced (null point) at 40 cm from the point $P$. The null point changed to 50 cm from the point $P$, when $16 \Omega$ resistance is connected in parallel to $R_2$. The values of resistances $R_1$ and $R_2$ are $\_\_\_\_$ .

A

$R_2=8 \Omega, R_1=\frac{16}{3} \Omega$

B

$R_2=12 \Omega, R_1=\frac{12}{3} \Omega$

C

$R_2=4 \Omega, R_1=\frac{4}{3} \Omega$

D

$R_2=16 \Omega, R_1=\frac{16}{3} \Omega$

Question 14: Palette 14/275

JEE Mains 2026 MCQ

Two known resistances of $R\ \Omega$ and $2R\ \Omega$ and one unknown resistance $X\ \Omega$ are connected in a circuit as shown in the figure. If the equivalent resistance between points $A$ and $B$ in the circuit is $X\ \Omega$, then the value of $X$ is __________ $\Omega$.

A

$2(\sqrt{3} - 1)R$

B

$R$

C

$(\sqrt{3} - 1)R$

D

$(\sqrt{3} + 1)R$

Question 15: Palette 15/275

JEE Mains 2026 MCQ

The total length of potentiometer wire AB is 50 cm in the arrangement as shown in the figure. If P is the point where the galvanometer shows zero reading then the length AP is ________ cm.

A

25

B

30

C

15

D

20

Question 16: Palette 16/275

JEE Mains 2026 MCQ

A battery with EMF $E$ and internal resistance $r$ is connected across a resistance $R$. The power consumption in $R$ will be maximum when:

A

$R = \sqrt{2} \, r$

B

$R = 2r$

C

$R = \frac{r}{2}$

D

$R = r$

Question 17: Palette 17/275

JEE Mains 2026 MCQ

Refer to the figure given below. The values of $I_1, I_2$ and $I_3$ are $\_\_\_\_$ .

A

$I_1=2.5 \mathrm{~A}, I_2=1.875 \mathrm{~A}, I_3=1.875 \mathrm{~A}$

B

$I_1=1.875 \mathrm{~A}, I_2=2.5 \mathrm{~A}, I_3=1.875 \mathrm{~A}$

C

$I_1=1.875 \mathrm{~A}, I_2=1.875 \mathrm{~A}, I_3=2.5 \mathrm{~A}$

D

$I_1=2.5 \mathrm{~A}, I_2=2.5 \mathrm{~A}, I_3=1.875 \mathrm{~A}$

Question 18: Palette 18/275

JEE Mains 2026 MCQ

Refer to the figure given below, current between terminals $A$ and $B$ is

$\_\_\_\_$ A.

A

12.5

B

1.25

C

7.5

D

5

Question 19: Palette 19/275

JEE Mains 2026 MCQ

A voltmeter with internal resistance of $x \Omega$ can be used to measure upto 20 V . In order to increase its measuring range to 30 V , the required modification is to $\_\_\_\_$ .

A

connect resistor of $\frac{x}{2} \Omega$, in series with voltmeter.

B

connect resistor of $\frac{x}{2} \Omega$, in parallel to voltmeter.

C

connect a resistor of $x \Omega$ in series with voltmeter.

D

connect resistor of $2 x \Omega$ in parallel to voltmeter.

Question 20: Palette 20/275

JEE Mains 2026 MCQ

The voltage and the current between $A$ and $B$ points shown in the circuit are $\_\_\_\_$ .

A

$ 24 \mathrm{~V}, 12 \mathrm{~A} $

B

$ 24 \mathrm{~V}, 4 \mathrm{~A} $

C

$ 18 \mathrm{~V}, 12 \mathrm{~A} $

D

$ 27 \mathrm{~V}, 4 \mathrm{~A} $

Question 21: Palette 21/275

JEE Mains 2026 MCQ

Two resistors of 200 $\Omega$ and 400 $\Omega$ are connected in series with a battery of 100 V. A bulb rated at 200 V, 100 W is connected across the 400 $\Omega$ resistance. The potential drop across the bulb is ________ V.

A

25

B

50

C

66.6

D

100

Question 22: Palette 22/275

JEE Mains 2025 MCQ

A wire of resistance $R$ is bent into a triangular pyramid as shown in figure with each segment having same length. The resistance between points $A$ and $B$ is $R / n$. The value of $n$ is :

A

16

B

10

C

12

D

14

Question 23: Palette 23/275

JEE Mains 2025 MCQ

There are ' $n$ ' number of identical electric bulbs, each is designed to draw a power $p$ independently from the mains supply. They are now joined in series across the mains supply. The total power drawn by the combination is :

A

np

B

p

C

$\frac{\mathrm{p}}{\mathrm{n}^2}$

D

$\frac{p}{n}$

Question 24: Palette 24/275

JEE Mains 2025 MCQ

From the combination of resistors with resistances values $R_1=R_2=R_3=5 \Omega$ and $R_4=10 \Omega$, which of the following combination is the best circuit to get an equivalent resistance of $6 \Omega$ ?

A

B

C

D

Question 25: Palette 25/275

JEE Mains 2025 MCQ

Current passing through a wire as function of time is given as $I(t)=0.02 t+0.01 \mathrm{~A}$. The charge that will flow through the wire from $t=1 \mathrm{~s}$ to $t=2 \mathrm{~s}$ is

A

0.02 C

B

0.07 C

C

0.06 C

D

0.04 C

Question 26: Palette 26/275

JEE Mains 2025 MCQ

A motor operating on 100 V draws a current of 1 A . If the efficiency of the motor is $91.6 \%$, then the loss of power in units of $\mathrm{cal} / \mathrm{s}$ is

A

6.2

B

2

C

8.4

D

4

Question 27: Palette 27/275

JEE Mains 2025 MCQ

A wire of length 25 m and cross-sectional area $5 \mathrm{~mm}^2$ having resistivity of $2 \times 10^{-6} \Omega \mathrm{~m}$ is bent into a complete circle. The resistance between diametrically opposite points will be

A

$100 \Omega$

B

$2.5 \Omega$

C

$12.5 \Omega$

D

$50 \Omega$

Question 28: Palette 28/275

JEE Mains 2025 MCQ

The battery of a mobile phone is rated as $4.2 \mathrm{~V}, 5800 \mathrm{~mAh}$. How much energy is stored ir it when fully charged?

A

87.7 kJ

B

43.8 kJ

C

48.7 kJ

D

24.4 kJ

Question 29: Palette 29/275

JEE Mains 2025 MCQ

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fittings. If household electric power is directly connected to a mercury tube, the tube will be damaged.

Reason (R): By using the choke coil, the voltage across the tube is reduced by a factor $\left(R / \sqrt{R^2+\omega^2 L^2}\right)$, where $\omega$ is frequency of the supply across resistor $R$ and inductor $L$. If the choke coil were not used, the voltage across the resistor would be the same as the applied voltage.

In the light of the above statements, choose the most appropriate answer from the options given below :

A

(A) is true but (R) is false

B

Both $(\mathbf{A})$ and $(\mathbf{R})$ are true and $(\mathbf{R})$ is the correct explanation of $(\mathbf{A})$ 3.

C

Both $(\mathbf{A})$ and $(\mathbf{R})$ are true but $(\mathbf{R})$ is not the correct explanation of $(\mathbf{A})$

D

(A) is false but (R) is true

Question 30: Palette 30/275

JEE Mains 2025 MCQ

In the circuit shown here, assuming threshold voltage of diode is negligibly small, then voltage $ V_{AB} $ is correctly represented by:

A

B

C

$ V_{AB} $ would be zero at all times.

D

Question 31: Palette 31/275

JEE Mains 2025 MCQ

Find the equivalent resistance between two ends of the following circuit

A

r

B

$\frac{\mathrm{r}}{6}$

C

$\frac{\mathrm{r}}{3}$

D

$\frac{r}{9}$

Question 32: Palette 32/275

JEE Mains 2025 MCQ

A wire of resistance R is bent into an equilateral triangle and an identical wire is bent into $a$ square. The ratio of resistance between the two end points of an edge of the triangle to that of the square is

A

$8 / 9$

B

$9 / 8$

C

$32 / 27$

D

$27 / 32$

Question 33: Palette 33/275

JEE Mains 2025 MCQ

A galvanometer having a coil of resistance $30 \Omega$ need 20 mA of current for full-scale deflection. If a maximum current of 3 A is to be measured using this galvanometer, the resistance of the shunt to be added to the galvanometer should be $\frac{30}{X} \Omega$, where $X$ is

A

447

B

298

C

149

D

596

Question 34: Palette 34/275

JEE Mains 2025 MCQ

Consider a moving coil galvanomenter (MCG):

A. The torsional constant in moving coil galvanometer has dimensions $\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]$

B. Increasing the current sensitivity may not necessarily increase the voltage sensitivity.

C. If we increase number of turns $(\mathrm{N})$ to its double $(2 \mathrm{~N})$, then the voltage sensitivity doubles.

D. MCG can be converted into an ammeter by introducing a shunt resistance of large value in parallel with galvanometer.

E. Current sensitivity of MCG depends inversely on number of turns of coil.

Choose the correct answer from the options given below:

A

A, D Only

B

A, B Only

C

A, B, E Only

D

B, D, E Only

Question 35: Palette 35/275

JEE Mains 2025 MCQ

Given below are two statements :

Statement-I : The equivalent emf of two nonideal batteries connected in parallel is smaller than either of the two emfs.

Statement-II : The equivalent internal resistance of two nonideal batteries connected in parallel is smaller than the internal resistance of either of the two batteries.

In the light of the above statements, choose the correct answer from the options given below.

A

Statement-I is false but Statement-II is true

B

Statement-I is true but Statement-II is false

C

Both Statement-I and Statement-II are false

D

Both Statement-I and Statement-II are true

Question 36: Palette 36/275

JEE Mains 2025 MCQ

Which of the following resistivity ( $\rho$ ) $\mathrm{v} / \mathrm{s}$ temperature ( T ) curves is most suitable to be used in wire bound standard resistors?

A

B

C

D

Question 37: Palette 37/275

JEE Mains 2025 MCQ

Sliding contact of a potentiometer is in the middle of the potentiometer wire having resistance $R_p=1 \Omega$ as shown in the figure. An external resistance of $R_e=2 \Omega$ is connected via the sliding contact. The electric current in the circuit is :

A

1.35 A

B

0.9 A

C

1.0 A

D

0.3 A

Question 38: Palette 38/275

JEE Mains 2024 MCQ

The effective resistance between $A$ and $B$, if resistance of each resistor is $R$, will be :

A

$\frac{8 R}{3}$

B

$\frac{4 R}{3}$

C

$\frac{2}{3} R$

D

$\frac{5 R}{3}$

Question 39: Palette 39/275

JEE Mains 2024 MCQ

A galvanometer has a coil of resistance $200 \Omega$ with a full scale deflection at $20 \mu \mathrm{A}$. The value of resistance to be added to use it as an ammeter of range $(0-20) \mathrm{mA}$ is :

A

$0.40\Omega$

B

$0.10\Omega$

C

$0.20\Omega$

D

$0.50\Omega$

Question 40: Palette 40/275

JEE Mains 2024 MCQ

The equivalent resistance between A and B is :

A

18 $\Omega$

B

27 $\Omega$

C

19 $\Omega$

D

25 $\Omega$

Question 41: Palette 41/275

JEE Mains 2024 MCQ

Water boils in an electric kettle in 20 minutes after being switched on. Using the same main supply, the length of the heating element should be _________ to __________ times of its initial length if the water is to be boiled in 15 minutes.

A

increased, $\frac{3}{4}$

B

increased, $\frac{4}{3}$

C

decreased, $\frac{3}{4}$

D

decreased, $\frac{4}{3}$

Question 42: Palette 42/275

JEE Mains 2024 MCQ

In the given circuit, the terminal potential difference of the cell is :

A

3 V

B

4 V

C

2 V

D

1.5 V

Question 43: Palette 43/275

JEE Mains 2024 MCQ

The number of electrons flowing per second in the filament of a $110 \mathrm{~W}$ bulb operating at $220 \mathrm{~V}$ is : (Given $\mathrm{e}=1.6 \times 10^{-19} \mathrm{C}$)

A

$1.25 \times 10^{19}$

B

$31.25 \times 10^{17}$

C

$6.25 \times 10^{18}$

D

$6.25 \times 10^{17}$

Question 44: Palette 44/275

JEE Mains 2024 MCQ

The value of unknown resistance $(x)$ for which the potential difference between $B$ and $D$ will be zero in the arrangement shown, is :

A

3 $\Omega$

B

42 $\Omega$

C

6 $\Omega$

D

9 $\Omega$

Question 45: Palette 45/275

JEE Mains 2024 MCQ

The ratio of heat dissipated per second through the resistance $5 \Omega$ and $10 \Omega$ in the circuit given below is:

A

4 : 1

B

2 : 1

C

1 : 2

D

1 : 1

Question 46: Palette 46/275

JEE Mains 2024 MCQ

A galvanometer of resistance $100 \Omega$ when connected in series with $400 \Omega$ measures a voltage of upto $10 \mathrm{~V}$. The value of resistance required to convert the galvanometer into ammeter to read upto $10 \mathrm{~A}$ is $x \times 10^{-2} \Omega$. The value of $x$ is :

A

2

B

20

C

800

D

200

Question 47: Palette 47/275

JEE Mains 2024 MCQ

In the given figure $\mathrm{R}_1=10 \Omega, \mathrm{R}_2=8 \Omega, \mathrm{R}_3=4 \Omega$ and $\mathrm{R}_4=8 \Omega$. Battery is ideal with emf $12 \mathrm{~V}$. Equivalent resistant of the circuit and current supplied by battery are respectively :

A

$12 \Omega$ and $11.4 \mathrm{~A}$

B

$10.5 \Omega$ and $1.14 \mathrm{~A}$

C

$10.5 \Omega$ and $1 \mathrm{~A}$

D

$12 \Omega$ and $1 \mathrm{~A}$

Question 48: Palette 48/275

JEE Mains 2024 MCQ

An electric bulb rated $50 \mathrm{~W}-200 \mathrm{~V}$ is connected across a $100 \mathrm{~V}$ supply. The power dissipation of the bulb is:

A

100 W

B

50 W

C

12.5 W

D

25 W

Question 49: Palette 49/275

JEE Mains 2024 MCQ

To measure the internal resistance of a battery, potentiometer is used. For $R=10 \Omega$, the balance point is observed at $l=500 \mathrm{~cm}$ and for $\mathrm{R}=1 \Omega$ the balance point is observed at $l=400 \mathrm{~cm}$. The internal resistance of the battery is approximately :

A

$0.1 \Omega$

B

$0.3 \Omega$

C

$0.2 \Omega$

D

$0.4 \Omega$

Question 50: Palette 50/275

JEE Mains 2024 MCQ

In a metre-bridge when a resistance in the left gap is $2 \Omega$ and unknown resistance in the right gap, the balance length is found to be $40 \mathrm{~cm}$. On shunting the unknown resistance with $2 \Omega$, the balance length changes by :

A

$62.5 $

B

$22.5 \mathrm{~cm}$

C

$20 \mathrm{~cm}$

D

$65 \mathrm{~cm}$

Question 51: Palette 51/275

JEE Mains 2024 MCQ

In an ammeter, $5 \%$ of the main current passes through the galvanometer. If resistance of the galvanometer is $\mathrm{G}$, the resistance of ammeter will be :

A

$199 \mathrm{~G}$

B

$200 \mathrm{~G}$

C

$\frac{G}{20}$

D

$\frac{\mathrm{G}}{199}$

Question 52: Palette 52/275

JEE Mains 2024 MCQ

The reading in the ideal voltmeter $(\mathrm{V})$ shown in the given circuit diagram is :

A

$3 \mathrm{~V}$

B

$10 \mathrm{~V}$

C

$5 \mathrm{~V}$

D

$0 \mathrm{~V}$

Question 53: Palette 53/275

JEE Mains 2024 MCQ

A galvanometer has a resistance of $50 ~\Omega$ and it allows maximum current of $5 \mathrm{~mA}$. It can be converted into voltmeter to measure upto $100 \mathrm{~V}$ by connecting in series a resistor of resistance :

A

$19500 \Omega$

B

$5975 \Omega$

C

$20050 \Omega$

D

$19950 \Omega$

Question 54: Palette 54/275

JEE Mains 2024 MCQ

By what percentage will the illumination of the lamp decrease if the current drops by 20%?

A

26%

B

36%

C

46%

D

56%

Question 55: Palette 55/275

JEE Mains 2024 MCQ

The resistance per centimeter of a meter bridge wire is $r$, with $X \Omega$ resistance in left gap. Balancing length from left end is at $40 \mathrm{~cm}$ with $25 \Omega$ resistance in right gap. Now the wire is replaced by another wire of $2 r$ resistance per centimeter. The new balancing length for same settings will be at

A

10 cm

B

80 cm

C

40 cm

D

20 cm

Question 56: Palette 56/275

JEE Mains 2024 MCQ

Two conductors have the same resistances at $0^{\circ} \mathrm{C}$ but their temperature coefficients of resistance are $\alpha_1$ and $\alpha_2$. The respective temperature coefficients for their series and parallel combinations are :

A

$\alpha_1+\alpha_2, \frac{\alpha_1 \alpha_2}{\alpha_1+\alpha_2}$

B

$\frac{\alpha_1+\alpha_2}{2}, \frac{\alpha_1+\alpha_2}{2}$

C

$\alpha_1+\alpha_2, \frac{\alpha_1+\alpha_2}{2}$

D

$\frac{\alpha_1+\alpha_2}{2}, \alpha_1+\alpha_2$

Question 57: Palette 57/275

JEE Mains 2024 MCQ

When a potential difference $V$ is applied across a wire of resistance $R$, it dissipates energy at a rate $W$. If the wire is cut into two halves and these halves are connected mutually parallel across the same supply, the energy dissipation rate will become:

A

1/2W

B

4W

C

1/4W

D

2W

Question 58: Palette 58/275

JEE Mains 2024 MCQ

A potential divider circuit is shown in figure. The output voltage V$_0$ is :

A

2 mV

B

4 V

C

0.5 V

D

12 mV

Question 59: Palette 59/275

JEE Mains 2024 MCQ

An electric toaster has resistance of $60 \Omega$ at room temperature $\left(27^{\circ} \mathrm{C}\right)$. The toaster is connected to a $220 \mathrm{~V}$ supply. If the current flowing through it reaches $2.75 \mathrm{~A}$, the temperature attained by toaster is around : ( if $\alpha=2 \times 10^{-4}$/$^\circ \mathrm{C}$)

A

1235 $^\circ$C

B

1667 $^\circ$C

C

694 $^\circ$C

D

1694 $^\circ$C

Question 60: Palette 60/275

JEE Mains 2024 MCQ

In the given circuit, the current in resistance R$_3$ is :

A

2 A

B

1.5 A

C

1 A

D

2.5 A

Question 61: Palette 61/275

JEE Mains 2024 MCQ

The deflection in moving coil galvanometer falls from 25 divisions to 5 division when a shunt of $24 \Omega$ is applied. The resistance of galvanometer coil will be :

A

$48 \Omega$

B

$100 \Omega$

C

$96 \Omega$

D

$12 \Omega$

Question 62: Palette 62/275

JEE Mains 2024 MCQ

A galvanometer having coil resistance $10 \Omega$ shows a full scale deflection for a current of $3 \mathrm{~mA}$. For it to measure a current of $8 \mathrm{~A}$, the value of the shunt should be:

A

$3.75 \times 10^{-3} \Omega$

B

$3 \times 10^{-3} \Omega$

C

$4.85 \times 10^{-3} \Omega$

D

$2.75 \times 10^{-3} \Omega$

Question 63: Palette 63/275

JEE Mains 2024 MCQ

The electric current through a wire varies with time as $I=I_0+\beta t$, where $I_0=20 \mathrm{~A}$ and $\beta=3 \mathrm{~A} / \mathrm{s}$. The amount of electric charge crossed through a section of the wire in $20 \mathrm{~s}$ is :

A

80 C

B

800 C

C

1000 C

D

1600 C

Question 64: Palette 64/275

JEE Mains 2024 MCQ

Three voltmeters, all having different internal resistances are joined as shown in figure. When some potential difference is applied across $A$ and $B$, their readings are $V_1, V_2$ and $V_3$. Choose the correct option.

A

$V_1=V_2$

B

$V_1 \neq V_3-V_2$

C

$V_1+V_2=V_3$

D

$V_1+V_2>V_3$

Question 65: Palette 65/275

JEE Mains 2024 MCQ

A current of $200 \mu \mathrm{A}$ deflects the coil of a moving coil galvanometer through $60^{\circ}$. The current to cause deflection through $\frac{\pi}{10}$ radian is :

A

120 $\mu$A

B

180 $\mu$A

C

30 $\mu$A

D

60 $\mu$A

Question 66: Palette 66/275

JEE Mains 2024 MCQ

Wheatstone bridge principle is used to measure the specific resistance $\left(S_1\right)$ of given wire, having length $L$, radius $r$. If $X$ is the resistance of wire, then specific resistance is ; $S_1=X\left(\frac{\pi r^2}{L}\right)$. If the length of the wire gets doubled then the value of specific resistance will be :

A

$\frac{S_1}{4}$

B

$2 \mathrm{~S}_1$

C

$\frac{\mathrm{S}_1}{2}$

D

$S_1$

Question 67: Palette 67/275

JEE Mains 2024 MCQ

A wire of length $10 \mathrm{~cm}$ and radius $\sqrt{7} \times 10^{-4} \mathrm{~m}$ connected across the right gap of a meter bridge. When a resistance of $4.5 \Omega$ is connected on the left gap by using a resistance box, the balance length is found to be at $60 \mathrm{~cm}$ from the left end. If the resistivity of the wire is $\mathrm{R} \times 10^{-7} \Omega \mathrm{m}$, then value of $\mathrm{R}$ is :

A

63

B

70

C

66

D

35

Question 68: Palette 68/275

JEE Mains 2024 MCQ

A wire of resistance $\mathrm{R}$ and length $\mathrm{L}$ is cut into 5 equal parts. If these parts are joined parallely, then resultant resistance will be :

A

$\frac{1}{25} \mathrm{R}$

B

$\frac{1}{5} R$

C

25 R

D

5 R

Question 69: Palette 69/275

JEE Mains 2023 MCQ

For designing a voltmeter of range $50 \mathrm{~V}$ and an ammeter of range $10 \mathrm{~mA}$ using a galvanometer which has a coil of resistance $54 \Omega$ showing a full scale deflection for $1 \mathrm{~mA}$ as in figure.



(A) for voltmeter $R \approx 50 \mathrm{k} \Omega$

(B) for ammeter $\mathrm{r} \approx 0.2 \Omega$

(C) for ammeter $\mathrm{r}=6 \Omega$

(D) for voltmeter $R \approx 5 \mathrm{k} \Omega$

(E) for voltmeter $R \approx 500 \Omega$

Choose the correct answer from the options given below:

A

$(\mathrm{A})$ and $(\mathrm{C})$

B

(A) and (B)

C

(C) and (E)

D

(C) and (D)

Question 70: Palette 70/275

JEE Mains 2023 MCQ

Given below are two statements:

Statement I : The equivalent resistance of resistors in a series combination is smaller than least resistance used in the combination.

Statement II : The resistivity of the material is independent of temperature.

In the light of the above statements, choose the correct answer from the options given below :

A

Statement I is true but Statement II is false

B

Both Statement I and Statement II are true

C

Both Statement I and Statement II are false

D

Statement I is false but Statement II is true

Question 71: Palette 71/275

JEE Mains 2023 MCQ

Different combination of 3 resistors of equal resistance $\mathrm{R}$ are shown in the figures. The increasing order for power dissipation is:

A

$\mathrm{P}_{\mathrm{B}}<\mathrm{P}_{\mathrm{C}}<\mathrm{P}_{\mathrm{D}}<\mathrm{P}_{\mathrm{A}}$

B

$\mathrm{P}_{\mathrm{C}}<\mathrm{P}_{\mathrm{B}}<\mathrm{P}_{\mathrm{A}}<\mathrm{P}_{\mathrm{D}}$

C

$\mathrm{P}_{\mathrm{C}}<\mathrm{P}_{\mathrm{D}}<\mathrm{P}_{\mathrm{A}}<\mathrm{P}_{\mathrm{B}}$

D

$\mathrm{P}_{\mathrm{A}}<\mathrm{P}_{\mathrm{B}}<\mathrm{P}_{\mathrm{C}}<\mathrm{P}_{\mathrm{D}}$

Question 72: Palette 72/275

JEE Mains 2023 MCQ

A wire of resistance $160 ~\Omega$ is melted and drawn in a wire of one-fourth of its length. The new resistance of the wire will be

A

$640 ~\Omega$

B

$40 ~\Omega$

C

$16 ~\Omega$

D

$10 ~\Omega$

Question 73: Palette 73/275

JEE Mains 2023 MCQ

The current flowing through R$_2$ is :

A

$\frac{1}{2} \mathrm{~A}$

B

$\frac{1}{3} \mathrm{~A}$

C

$\frac{1}{4} \mathrm{~A}$

D

$\frac{2}{3} \mathrm{~A}$

Question 74: Palette 74/275

JEE Mains 2023 MCQ

Two identical heater filaments are connected first in parallel and then in series. At the same applied voltage, the ratio of heat produced in same time for parallel to series will be:

A

4 : 1

B

1 : 4

C

2 : 1

D

1 : 2

Question 75: Palette 75/275

JEE Mains 2023 MCQ

The current sensitivity of moving coil galvanometer is increased by $25 \%$. This increase is achieved only by changing in the number of turns of coils and area of cross section of the wire while keeping the resistance of galvanometer coil constant. The percentage change in the voltage sensitivity will be:

A

+25%

B

$-$50%

C

$-$25%

D

Zero

Question 76: Palette 76/275

JEE Mains 2023 MCQ

The equivalent resistance of the circuit shown below between points a and b is :

A

16$\Omega$

B

20$\Omega$

C

3.2$\Omega$

D

24$\Omega$

Question 77: Palette 77/275

JEE Mains 2023 MCQ

The equivalent resistance between A and B as shown in figure is:

A

$30 ~\mathrm{k} \Omega$

B

$20 ~\mathrm{k} \Omega$

C

$5 ~\mathrm{k} \Omega$

D

$10 ~\mathrm{k} \Omega$

Question 78: Palette 78/275

JEE Mains 2023 MCQ

Figure shows a part of an electric circuit. The potentials at points $a, b$ and $c$ are $30 \mathrm{~V}, 12 \mathrm{~V}$ and $2 \mathrm{~V}$ respectively. The current through the $20 ~\Omega$ resistor will be,

A

0.2 A

B

0.6 A

C

0.4 A

D

1.0 A

Question 79: Palette 79/275

JEE Mains 2023 MCQ

A student is provided with a variable voltage source $\mathrm{V}$, a test resistor $R_{T}=10 ~\Omega$, two identical galvanometers $G_{1}$ and $G_{2}$ and two additional resistors, $R_{1}=10 ~M \Omega$ and $R_{2}=0.001 ~\Omega$. For conducting an experiment to verify ohm's law, the most suitable circuit is:

A

B

C

D

Question 80: Palette 80/275

JEE Mains 2023 MCQ

Given below are two statements : One is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$.

Assertion A : For measuring the potential difference across a resistance of $600 \Omega$, the voltmeter with resistance $1000 \Omega$ will be preferred over voltmeter with resistance $4000 \Omega$.

Reason R : Voltmeter with higher resistance will draw smaller current than voltmeter with lower resistance.

In the light of the above statements, choose the most appropriate answer from the options given below.

A

$\mathbf{A}$ is not correct but $\mathbf{R}$ is correct

B

Both $\mathbf{A}$ and $\mathbf{R}$ are correct and $\mathbf{R}$ is the correct explanation of $\mathbf{A}$

C

$\mathbf{A}$ is correct but $\mathbf{R}$ is not correct

D

Both $\mathbf{A}$ and $\mathbf{R}$ are correct but $\mathbf{R}$ is not the correct explanation of $\mathbf{A}$

Question 81: Palette 81/275

JEE Mains 2023 MCQ

Equivalent resistance between the adjacent corners of a regular n-sided polygon of uniform wire of resistance R would be :

A

$\frac{(\mathrm{n}-1) \mathrm{R}}{\mathrm{n}^{2}}$

B

$\frac{n^{2} R}{n-1}$

C

$\frac{(n-1) R}{(2 n-1)}$

D

$\frac{(n-1) R}{n}$

Question 82: Palette 82/275

JEE Mains 2023 MCQ

The equivalent resistance between $A$ and $B$ of the network shown in figure;

A

21 R

B

$\frac{8}{3}$ R

C

11$\frac{2}{3}$ R

D

14 R

Question 83: Palette 83/275

JEE Mains 2023 MCQ

The number of turns of the coil of a moving coil galvanometer is increased in order to increase current sensitivity by $50 \%$. The percentage change in voltage sensitivity of the galvanometer will be :

A

$0 \%$

B

$75 \%$

C

$100 \%$

D

$50 \%$

Question 84: Palette 84/275

JEE Mains 2023 MCQ

The $\mathrm{H}$ amount of thermal energy is developed by a resistor in $10 \mathrm{~s}$ when a current of $4 \mathrm{~A}$ is passed through it. If the current is increased to $16 \mathrm{~A}$, the thermal energy developed by the resistor in $10 \mathrm{~s}$ will be :

A

$\frac{\mathrm{H}}{4}$

B

$16 \mathrm{H}$

C

H

D

$4 \mathrm{H}$

Question 85: Palette 85/275

JEE Mains 2023 MCQ

The drift velocity of electrons for a conductor connected in an electrical circuit is $\mathrm{V}_{\mathrm{d}}$. The conductor in now replaced by another conductor with same material and same length but double the area of cross section. The applied voltage remains same. The new drift velocity of electrons will be

A

$\frac{V_{d}}{4}$

B

$\mathrm{V}_{\mathrm{d}}$

C

$2 \mathrm{~V}_{\mathrm{d}}$

D

$\frac{V_{d}}{2}$

Question 86: Palette 86/275

JEE Mains 2023 MCQ

The equivalent resistance between $A$ and $B$ is _________.

A

$\frac{1}{2} \Omega$

B

$\frac{2}{3} \Omega$

C

$\frac{3}{2} \Omega$

D

$\frac{1}{3} \Omega$

Question 87: Palette 87/275

JEE Mains 2023 MCQ

The charge flowing in a conductor changes with time as $\mathrm{Q}(\mathrm{t})=\alpha \mathrm{t}-\beta \mathrm{t}^{2}+\gamma \mathrm{t}^{3}$. Where $\alpha, \beta$ and $\gamma$ are constants. Minimum value of current is :

A

$\beta-\frac{\alpha^{2}}{3 \gamma}$

B

$\alpha-\frac{3 \beta^{2}}{\gamma}$

C

$\alpha-\frac{\beta^{2}}{3 \gamma}$

D

$\alpha-\frac{\gamma^{2}}{3 \beta}$

Question 88: Palette 88/275

JEE Mains 2023 MCQ

With the help of potentiometer, we can determine the value of emf of a given cell. The sensitivity of the potentiometer is

(A) directly proportional to the length of the potentiometer wire

(B) directly proportional to the potential gradient of the wire

(C) inversely proportional to the potential gradient of the wire

(D) inversely proportional to the length of the potentiometer wire

Choose the correct option for the above statements :

A

A only

B

B and D only

C

A and C only

D

inversely C only

Question 89: Palette 89/275

JEE Mains 2023 MCQ

Ratio of thermal energy released in two resistors R and 3R connected in parallel in an electric circuit is :

A

1 : 1

B

1 : 27

C

1 : 3

D

3 : 1

Question 90: Palette 90/275

JEE Mains 2023 MCQ

The resistance of a wire is 5 $\Omega$. It's new resistance in ohm if stretched to 5 times of it's original length will be :

A

25

B

625

C

5

D

125

Question 91: Palette 91/275

JEE Mains 2023 MCQ

A uniform metallic wire carries a current 2 A, when 3.4 V battery is connected across it. The mass of uniform metallic wire is 8.92 $\times$ 10$^{-3}$ kg, density is 8.92 $\times$ 10$^{3}$ kg/m$^3$ and resistivity is 1.7 $\times$ 10$^{-8}~\Omega$-$\mathrm{m}$. The length of wire is :

A

$l=100$ m

B

$l=6.8$ m

C

$l=5$ m

D

$l=10$ m

Question 92: Palette 92/275

JEE Mains 2023 MCQ

A cell of emf 90 V is connected across series combination of two resistors each of 100$\Omega$ resistance. A voltmeter of resistance 400$\Omega$ is used to measure the potential difference across each resistor. The reading of the voltmeter will be :

A

40 V

B

90 V

C

45 V

D

80 V

Question 93: Palette 93/275

JEE Mains 2023 MCQ

As shown in the figure, a network of resistors is connected to a battery of 24V with an internal resistance of 3 $\Omega$. The currents through the resistors R$_4$ and R$_5$ are I$_4$ and I$_5$ respectively. The values of I$_4$ and I$_5$ are :

A

$\mathrm{I_4=\frac{8}{5}A}$ and $\mathrm{I_5=\frac{2}{5}A}$

B

$\mathrm{I_4=\frac{6}{5}A}$ and $\mathrm{I_5=\frac{24}{5}A}$

C

$\mathrm{I_4=\frac{2}{5}A}$ and $\mathrm{I_5=\frac{8}{5}A}$

D

$\mathrm{I_4=\frac{24}{5}A}$ and $\mathrm{I_5=\frac{6}{5}A}$

Question 94: Palette 94/275

JEE Mains 2022 MCQ

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: Alloys such as constantan and manganin are used in making standard resistance coils.

Reason R: Constantan and manganin have very small value of temperature coefficient of resistance.

In the light of the above statements, choose the correct answer from the options given below.

A

Both A and R are true and R is the correct explanation of A.

B

Both A and R are true but R is NOT the correct explanation of A.

C

A is true but R is false.

D

A is false but R is true.

Question 95: Palette 95/275

JEE Mains 2022 MCQ

A $1 \mathrm{~m}$ long wire is broken into two unequal parts $\mathrm{X}$ and $\mathrm{Y}$. The $\mathrm{X}$ part of the wire is streched into another wire W. Length of $W$ is twice the length of $X$ and the resistance of $\mathrm{W}$ is twice that of $\mathrm{Y}$. Find the ratio of length of $\mathrm{X}$ and $\mathrm{Y}$.

A

1 : 4

B

1 : 2

C

4 : 1

D

2 : 1

Question 96: Palette 96/275

JEE Mains 2022 MCQ

Two metallic wires of identical dimensions are connected in series. If $\sigma_{1}$ and $\sigma_{2}$ are the conductivities of the these wires respectively, the effective conductivity of the combination is :

A

$ \frac{\sigma_{1} \sigma_{2}}{\sigma_{1}+\sigma_{2}} $

B

$ \frac{2 \sigma_{1} \sigma_{2}}{\sigma_{1}+\sigma_{2}} $

C

$ \frac{\sigma_{1}+\sigma_{2}}{2 \sigma_{1} \sigma_{2}} $

D

$ \frac{\sigma_{1}+\sigma_{2}}{\sigma_{1} \sigma_{2}} $

Question 97: Palette 97/275

JEE Mains 2022 MCQ

Given below are two statements :

Statement I : A uniform wire of resistance $80 \,\Omega$ is cut into four equal parts. These parts are now connected in parallel. The equivalent resistance of the combination will be $5 \,\Omega$.

Statement II: Two resistances 2R and 3R are connected in parallel in a electric circuit. The value of thermal energy developed in 3R and 2R will be in the ratio $3: 2$.

In the light of the above statements, choose the most appropriate answer from the option given below

A

Both statement I and statement II are correct

B

Both statement I and statement II are incorrect

C

Statement I is correct but statement II is incorrect

D

Statement I is incorrect but statement II is correct

Question 98: Palette 98/275

JEE Mains 2022 MCQ

A wire of resistance R₁ is drawn out so that its length is increased by twice of its original length. The ratio of new resistance to original resistance is :

A

9 : 1

B

1 : 9

C

4 : 1

D

3 : 1

Question 99: Palette 99/275

JEE Mains 2022 MCQ

(A) The drift velocity of electrons decreases with the increase in the temperature of conductor.

(B) The drift velocity is inversely proportional to the area of cross-section of given conductor.

(C) The drift velocity does not depend on the applied potential difference to the conductor.

(D) The drift velocity of electron is inversely proportional to the length of the conductor.

(E) The drift velocity increases with the increase in the temperature of conductor.

Choose the correct answer from the options given below :

A

(A) and (B) only

B

(A) and (D) only

C

(B) and (E) only

D

(B) and (C) only

Question 100: Palette 100/275

JEE Mains 2022 MCQ

Two sources of equal emfs are connected in series. This combination is connected to an external resistance R. The internal resistances of the two sources are $r_{1}$ and $r_{2}$ $\left(r_{1}>r_{2}\right)$. If the potential difference across the source of internal resistance $r_{1}$ is zero, then the value of R will be :

A

$r_{1}-r_{2}$

B

$\frac{r_{1} r_{2}}{r_{1}+r_{2}}$

C

$\frac{r_{1}+r_{2}}{2}$

D

$r_{2}-r_{1}$

Question 101: Palette 101/275

JEE Mains 2022 MCQ

A battery of $6 \mathrm{~V}$ is connected to the circuit as shown below. The current I drawn from the battery is :

A

1A

B

2A

C

$\frac{6}{11}$ A

D

$\frac{4}{3}$ A

Question 102: Palette 102/275

JEE Mains 2022 MCQ

The current I in the given circuit will be :

A

10 A

B

20 A

C

4 A

D

40 A

Question 103: Palette 103/275

JEE Mains 2022 MCQ

A current of 15 mA flows in the circuit as shown in figure. The value of potential difference between the points A and B will be:

A

50 V

B

75 V

C

150 V

D

275 V

Question 104: Palette 104/275

JEE Mains 2022 MCQ

Which of the following physical quantities have the same dimensions?

A

Electric displacement $(\overrightarrow{\mathrm{D}})$ and surface charge density

B

Displacement current and electric field

C

Current density and surface charge density

D

Electric potential and energy

Question 105: Palette 105/275

JEE Mains 2022 MCQ

An electric cable of copper has just one wire of radius 9 mm. Its resistance is 14 $\Omega$. If this single copper wire of the cable is replaced by seven identical well insulated copper wires each of radius 3 mm connected in parallel, then the new resistance of the combination will be :

A

9 $\Omega$

B

18 $\Omega$

C

28 $\Omega$

D

126 $\Omega$

Question 106: Palette 106/275

JEE Mains 2022 MCQ

The combination of two identical cells, whether connected in series or parallel combination provides the same current through an external resistance of 2$\Omega$. The value of internal resistance of each cell is

A

2$\Omega$

B

4$\Omega$

C

6$\Omega$

D

8$\Omega$

Question 107: Palette 107/275

JEE Mains 2022 MCQ

Resistance of the wire is measured as 2 $\Omega$ and 3 $\Omega$ at 10$^\circ$C and 30$^\circ$C respectively. Temperature co-efficient of resistance of the material of the wire is :

A

0.033 $^\circ$C^$-$1

B

$-$0.033 $^\circ$C^$-$1

C

0.011 $^\circ$C^$-$1

D

0.055 $^\circ$C^$-$1

Question 108: Palette 108/275

JEE Mains 2022 MCQ

A 72 $\Omega$ galvanometer is shunted by a resistance of 8 $\Omega$. The percentage of the total current which passes through the galvanometer is :

A

0.1%

B

10%

C

25%

D

0.25%

Question 109: Palette 109/275

JEE Mains 2022 MCQ

The equivalent resistance between points A and B in the given network is :

A

65$\Omega$

B

20$\Omega$

C

5$\Omega$

D

2$\Omega$

Question 110: Palette 110/275

JEE Mains 2022 MCQ

An aluminium wire is stretched to make its length, 0.4% larger. The percentage change in resistance is :

A

0.4%

B

0.2%

C

0.8%

D

0.6%

Question 111: Palette 111/275

JEE Mains 2022 MCQ

Two cells of same emf but different internal resistances r₁ and r₂ are connected in series with a resistance R. The value of resistance R, for which the potential difference across second cell is zero, is :

A

r₂ $-$ r₁

B

r₁ $-$ r₂

C

r₁

D

r₂

Question 112: Palette 112/275

JEE Mains 2022 MCQ

If n represents the actual number of deflections in a converted galvanometer of resistance G and shunt resistance S. Then the total current I when its figure of merit is K will be:

A

${{KS} \over {(S + G)}}$

B

${{(G + S)} \over {nKS}}$

C

${{nKS} \over {(G + S)}}$

D

${{nK(G + S)} \over S}$

Question 113: Palette 113/275

JEE Mains 2022 MCQ

A teacher in his physics laboratory allotted an experiment to determine the resistance (G) of a galvanometer. Students took the observations for ${1 \over 3}$ deflection in the galvanometer. Which of the below is true for measuring value of G?

A

${1 \over 3}$ deflection method cannot be used for determining the resistance of the galvanometer.

B

${1 \over 3}$ deflection method can be used and in this case the G equals to twice the value of shunt resistances.

C

${1 \over 3}$ deflection method can be used and in this case, the G equals to three times the value of shunt resistances.

D

${1 \over 3}$ deflection method can be used and in this case the G value equals to the shunt resistances.

Question 114: Palette 114/275

JEE Mains 2022 MCQ

What will be the most suitable combination of three resistors A = 2$\Omega$, B = 4$\Omega$, C = 6$\Omega$ so that $\left( {{{22} \over 3}} \right)$$\Omega$ is equivalent resistance of combination?

A

Parallel combination of A and C connected in series with B.

B

Parallel combination of A and B connected in series with C.

C

Series combination of A and C connected in parallel with B.

D

Series combination of B and C connected in parallel with A.

Question 115: Palette 115/275

JEE Mains 2022 MCQ

Two identical cells each of emf 1.5 V are connected in parallel across a parallel combination of two resistors each of resistance 20 $\Omega$. A voltmeter connected in the circuit measures 1.2 V. The internal resistance of each cell is :

A

2.5 $\Omega$

B

4 $\Omega$

C

5 $\Omega$

D

10 $\Omega$

Question 116: Palette 116/275

JEE Mains 2021 MCQ

Due to cold weather a 1 m water pipe of cross-sectional area 1 cm² is filled with ice at $-$10$^\circ$C. Resistive heating is used to melt the ice. Current of 0.5A is passed through 4 k$\Omega$ resistance. Assuming that all the heat produced is used for melting, what is the minimum time required? (Given latent heat of fusion for water/ice = 3.33 $\times$ 10⁵ J kg^$-$1, specific heat of ice = 2 $\times$ 10³ J kg^$-$1 and density of ice = 10³ kg/m³

A

0.353 s

B

35.3 s

C

3.53 s

D

70.6 s

Question 117: Palette 117/275

JEE Mains 2021 MCQ

Two resistors R₁ = (4 $\pm$ 0.8) $\Omega$ and R₂ = (4 $\pm$ 0.4) $\Omega$ are connected in parallel. The equivalent resistance of their parallel combination will be :

A

(4 $\pm$ 0.4) $\Omega$

B

(2 $\pm$ 0.4) $\Omega$

C

(2 $\pm$ 0.3) $\Omega$

D

(4 $\pm$ 0.3) $\Omega$

Question 118: Palette 118/275

JEE Mains 2021 MCQ

The equivalent resistance of the given circuit between the terminals A and B is :

A

0$\Omega$

B

3$\Omega$

C

${9 \over 2}$$\Omega$

D

1$\Omega$

Question 119: Palette 119/275

JEE Mains 2021 MCQ

Consider a galvanometer shunted with 5$\Omega$ resistance and 2% of current passes through it. What is the resistance of the given galvanometer ?

A

300 $\Omega$

B

344 $\Omega$

C

245 $\Omega$

D

226 $\Omega$

Question 120: Palette 120/275

JEE Mains 2021 MCQ

The Colour coding on a carbon resistor is shown in the given figure. The resistance value of the given resistor is :

A

(5700 $\pm$ 285) $\Omega$

B

(7500 $\pm$ 750) $\Omega$

C

(5700 $\pm$ 375) $\Omega$

D

(7500 $\pm$ 375) $\Omega$

Question 121: Palette 121/275

JEE Mains 2021 MCQ

For full scale deflection of total 50 divisions, 50 mV voltage is required in galvanometer. The resistance of galvanometer if its current sensitivity is 2 div/mA will be :

A

1$\Omega$

B

5$\Omega$

C

4$\Omega$

D

2$\Omega$

Question 122: Palette 122/275

JEE Mains 2021 MCQ

Five identical cells each of internal resistance 1$\Omega$ and emf 5V are connected in series and in parallel with an external resistance 'R'. For what value of 'R', current in series and parallel combination will remain the same?

A

1 $\Omega$

B

25 $\Omega$

C

5 $\Omega$

D

10 $\Omega$

Question 123: Palette 123/275

JEE Mains 2021 MCQ

If you are provided a set of resistances 2$\Omega$, 4$\Omega$, 6$\Omega$ and 8$\Omega$. Connect these resistances so as to obtain an equivalent resistance of ${{46} \over 3}$$\Omega$.

A

4$\Omega$ and 6$\Omega$ are in parallel with 2$\Omega$ and 8$\Omega$ in series

B

6$\Omega$ and 8$\Omega$ are in parallel with 2$\Omega$ and 4$\Omega$ in series

C

2$\Omega$ and 6$\Omega$ are in parallel with 4$\Omega$ and 8$\Omega$ in series

D

2$\Omega$ and 4$\Omega$ are in parallel with 6$\Omega$ and 8$\Omega$ in series

Question 124: Palette 124/275

JEE Mains 2021 MCQ

An electric bulb of 500 watt at 100 volt is used in a circuit having a 200 V supply. Calculate the resistance R to be connected in series with the bulb so that the power delivered by the bulb is 500 W.

A

20 $\Omega$

B

30 $\Omega$

C

5 $\Omega$

D

10 $\Omega$

Question 125: Palette 125/275

JEE Mains 2021 MCQ

In the given figure, the emf of the cell is 2.2 V and if internal resistance is 0.6$\Omega$. Calculate the power dissipated in the whole circuit :

A

1.32 W

B

0.65 W

C

2.2 W

D

4.4 W

Question 126: Palette 126/275

JEE Mains 2021 MCQ

What equal length of an iron wire and a copper-nickel alloy wire, each of 2 mm diameter connected parallel to give an equivalent resistance of 3$\Omega$ ?

(Given resistivities of iron and copper-nickel alloy wire are 12 $\mu$$\Omega$ and 51 $\mu$$\Omega$ cm respectively)

A

82 m

B

97 m

C

110 m

D

90 m

Question 127: Palette 127/275

JEE Mains 2021 MCQ

The resistance of a conductor at 15$^\circ$C is 16$\Omega$ and at 100$^\circ$C is 20$\Omega$. What will be the temperature coefficient of resistance of the conductor?

A

0.010$^\circ$C^$-$1

B

0.033$^\circ$C^$-$1

C

0.003$^\circ$C^$-$1

D

0.042$^\circ$C^$-$1

Question 128: Palette 128/275

JEE Mains 2021 MCQ

In the given figure, a battery of emf E is connected across a conductor PQ of length 'l' and different area of cross-sections having radii r₁ and r₂ (r₂ < r₁).


Choose the correct option as one moves from P to Q :

A

Drift velocity of electron increases.

B

Electric field decreases.

C

Electron current decreases.

D

All of these

Question 129: Palette 129/275

JEE Mains 2021 MCQ

In the given potentiometer circuit arrangement, the balancing length AC is measured to be 250 cm. When the galvanometer connection is shifted from point (1) to point (2) in the given diagram, the balancing length becomes 400 cm. The ratio of the emf of two cells, ${{{\varepsilon _1}} \over {{\varepsilon _2}}}$ is :

A

${5 \over 3}$

B

${8 \over 5}$

C

${4 \over 3}$

D

${3 \over 2}$

Question 130: Palette 130/275

JEE Mains 2021 MCQ

The given potentiometer has its wire of resistance 10$\Omega$. When the sliding contact is in the middle of the potentiometer wire, the potential drop across 2$\Omega$ resistor is :

A

10 V

B

5 V

C

${{40} \over 9}$ V

D

${{40} \over 11}$ V

Question 131: Palette 131/275

JEE Mains 2021 MCQ

In the given figure, there is a circuit of potentiometer of length AB = 10 m. The resistance per unit length is 0.1 $\Omega$ per cm. Across AB, a battery of emf E and internal resistance 'r' is connected. The maximum value of emf measured by this potentiometer is :

A

5 V

B

2.25 V

C

6 V

D

2.75 V

Question 132: Palette 132/275

JEE Mains 2021 MCQ

A Copper (Cu) rod of length 25 cm and cross-sectional area 3 mm² is joined with a similar Aluminium (Al) rod as shown in figure. Find the resistance of the combination between the ends A and B.

(Take Resistivity of Copper = 1.7 $\times$ 10^$-$8 $\Omega$m and Resistivity of Aluminium = 2.6 $\times$ 10^$-$8 $\Omega$m)

A

0.0858 m$\Omega$

B

1.420 m$\Omega$

C

0.858 m$\Omega$

D

2.170 m$\Omega$

Question 133: Palette 133/275

JEE Mains 2021 MCQ

A current of 5 A is passing through a non-linear magnesium wire of cross-section 0.04 m². At every point the direction of current density is at an angle of 60$^\circ$ with the unit vector of area of cross-section. The magnitude of electric field at every point of the conductor is :

(Resistivity of magnesium $\rho$ = 44 $\times$ 10^$-$8 $\Omega$m)

A

11 $\times$ 10^$-$5 V/m

B

11 $\times$ 10^$-$3 V/m

C

11 $\times$ 10^$-$7 V/m

D

11 $\times$ 10^$-$2 V/m

Question 134: Palette 134/275

JEE Mains 2021 MCQ

The value of current in the 6 $\Omega$ resistance is :

A

4A

B

8A

C

10A

D

6A

Question 135: Palette 135/275

JEE Mains 2021 MCQ

In the experiment of Ohm's law, a potential difference of 5.0 V is applied across the end of a conductor of length 10.0 cm and diameter of 5.00 mm. The measured current in the conductor is 2.00 A. The maximum permissible percentage error in the resistivity of the conductor is :

A

3.9

B

8.4

C

7.5

D

3.0

Question 136: Palette 136/275

JEE Mains 2021 MCQ

Two cells of emf 2E and E with internal resistance r₁ and r₂ respectively are connected in series to an external resistor R (see figure). The value of R, at which the potential difference across the terminals of the first cell becomes zero is

A

r₁ $-$ r₂

B

${{{r_1}} \over 2} - {r_2}$

C

${{{r_1}} \over 2} + {r_2}$

D

r₁ + r₂

Question 137: Palette 137/275

JEE Mains 2021 MCQ

The four arms of a Wheatstone bridge have resistances as shown in the figure. A galvanometer of 15$\Omega$ resistance is connected across BD. Calculate the current through the galvanometer when a potential difference of 10V is maintained across AC.

A

4.87 $\mu$A

B

4.87 mA

C

2.44 mA

D

2.44 $\mu$A

Question 138: Palette 138/275

JEE Mains 2021 MCQ

A current of 10A exists in a wire of cross-sectional area of 5 mm² with a drift velocity of 2 $\times$ 10^$-$3 ms^$-$1. The number of free electrons in each cubic meter of the wire is ___________.

A

625 $\times$ 10²⁵

B

1 $\times$ 10²³

C

2 $\times$ 10²⁵

D

2 $\times$ 10⁶

Question 139: Palette 139/275

JEE Mains 2021 MCQ

A resistor develops 500 J of thermal energy in 20 s when a current of 1.5A is passed through it. If the current is increased from 1.5A to 3A, what will be the energy developed in 20 s.

A

1000 J

B

2000 J

C

1500 J

D

500 J

Question 140: Palette 140/275

JEE Mains 2021 MCQ

A conducting wire of length 'l', area of cross-section A and electric resistivity $\rho$ is connected between the terminals of a battery. A potential difference V is developed between its ends, causing an electric current.

If the length of the wire of the same material is doubled and the area of cross-section is halved, the resultant current would be :

A

$4{{VA} \over {\rho l}}$

B

${3 \over 4}{{VA} \over {\rho l}}$

C

${1 \over 4}{{VA} \over {\rho l}}$

D

${1 \over 4}{{\rho l} \over {VA}}$

Question 141: Palette 141/275

JEE Mains 2021 MCQ

A wire of 1$\Omega$ has a length of 1 m. It is stretched till its length increases by 25%. The percentage change in resistance to the nearest integer is :

A

76%

B

12.5%

C

25%

D

56%

Question 142: Palette 142/275

JEE Mains 2021 MCQ

Five equal resistances are connected in a network as shown in figure. The net resistance between the points A and B is :

A

${{3R} \over 2}$

B

${{R} \over 2}$

C

2R

D

R

Question 143: Palette 143/275

JEE Mains 2021 MCQ

A current through a wire depends on time as

i = $\alpha$₀t + $\beta$t²

where $\alpha$₀ = 20 A/s and $\beta$ = 8 As^$-$2. Find the charge crossed through a section of the wire in 15 s.

A

2250 C

B

2100 C

C

260 C

D

11250 C

Question 144: Palette 144/275

JEE Mains 2021 MCQ

A cell E₁ of emf 6V and internal resistance 2$\Omega$ is connected with another cell E₂ of emf 4V and internal resistance 8$\Omega$ (as shown in the figure). The potential difference across points X and Y is :

A

10.0 V

B

2.0 V

C

5.6 V

D

3.6 V

Question 145: Palette 145/275

JEE Mains 2020 MCQ

A circuit to verify Ohm's law uses ammeter and voltmeter in series or parallel connected correctly to the resistor. In the circuit :

A

Ammeter is always connected in series and voltmeter in parallel

B

Both ammeter and voltmeter must be connected in series

C

Both ammeter and voltmeter must be connected in parallel

D

Ammeter is always used in parallel and voltmeter is series

Question 146: Palette 146/275

JEE Mains 2020 MCQ

In the figure shown, the current in the 10 V battery is close to :

A

0.36 A from negative to positive terminal

B

0.42 A from positive to negative terminal

C

0.71 A from positive to negative terminal

D

0.21 A from positive to negative terminal

Question 147: Palette 147/275

JEE Mains 2020 MCQ

A galvanometer is used in laboratory for detecting the null point in electrical experiments. If, on passing a current of 6 mA it produces a deflection of 2^o, its figure of merit is close to :

A

6 $ \times $ 10^–3 A/div

B

666^o A/div

C

3 $ \times $ 10^–3 A/div

D

333^o A/div

Question 148: Palette 148/275

JEE Mains 2020 MCQ

In the circuit, given in the figure currents in different branches and value of one resistor are shown. Then potential at point B with respect to the point A is :

A

+2 V

B

-2 V

C

+1 V

D

-1 V

Question 149: Palette 149/275

JEE Mains 2020 MCQ

An electrical power line, having a total resistance of 2 $\Omega $, delivers 1 kW at 220 V. The efficiency of the transmission line is approximately :

A

85%

B

96%

C

72%

D

91%

Question 150: Palette 150/275

JEE Mains 2020 MCQ

A galvanometer of resistance G is converted into a voltmeter of range 0 – 1 V by connecting a resistance R₁ in series with it. The additional resistance that should be connected in series with R₁ to increase the range of the voltmeter to 0 – 2 V will be :

A

G

B

R₁

C

R₁ + G

D

R₁ - G

Question 151: Palette 151/275

JEE Mains 2020 MCQ

The value of current i₁ flowing from A to C in the circuit diagram is :

A

1 A

B

4 A

C

5 A

D

2 A

Question 152: Palette 152/275

JEE Mains 2020 MCQ

A battery of 3.0 V is connected to a resistor dissipating 0.5 W of power. If the terminal voltage of the battery is 2.5 V, the power dissipated within the internal resistance is :

A

0.50 W

B

0.072 W

C

0.10 W

D

0.125 W

Question 153: Palette 153/275

JEE Mains 2020 MCQ

Two resistors 400$\Omega $ and 800$\Omega $ are connected in series across a 6 V battery. The potential difference measured by a voltmeter of 10 k$\Omega $ across 400 $\Omega $ resistor is close to :

A

2.05 V

B

1.95 V

C

2 V

D

1.8 V

Question 154: Palette 154/275

JEE Mains 2020 MCQ

Model a torch battery of length $l$ to be made up of a thin cylindrical bar of radius ‘a’ and a concentric thin cylindrical shell of radius ‘b’ filled in between with an electrolyte of resistivity $\rho $ (see figure). If the battery is connected to a resistance of value R, the maximum Joule heating in R will take place for :

A

$R = {{2\rho } \over {\pi l}}\ln \left( {{b \over a}} \right)$

B

$R = {\rho \over {\pi l}}\ln \left( {{b \over a}} \right)$

C

$R = {\rho \over {2\pi l}}\ln \left( {{b \over a}} \right)$

D

$R = {\rho \over {2\pi l}}\left( {{b \over a}} \right)$

Question 155: Palette 155/275

JEE Mains 2020 MCQ

A potentiometer wire PQ of 1 m length is connected to a standard cell E₁. Another cell E₂ of emf 1.02 V is connected with a resistance ‘r’ and switch S (as shown in figure). With switch S open, the null position is obtained at a distance of 49 cm from Q. The potential gradient in the potentiometer wire is :

A

0.04 V/cm

B

0.01 V/cm

C

0.02 V/cm

D

0.03 V/cm

Question 156: Palette 156/275

JEE Mains 2020 MCQ

Consider four conducting materials copper, tungsten, mercury and aluminium with resistivity $\rho $_C, $\rho $_T, $\rho $_M and $\rho $_A respectively. Then :

A

$\rho $_C > $\rho $_A > $\rho $_T

B

$\rho $_M > $\rho $_A > $\rho $_C

C

$\rho $_A > $\rho $_T > $\rho $_C

D

$\rho $_A > $\rho $_M > $\rho $_C

Question 157: Palette 157/275

JEE Mains 2020 MCQ

In the given circuit diagram, a wire is joining points B and D. The current in this wire is :

A

4 A

B

2 A

C

zero

D

0.4 A

Question 158: Palette 158/275

JEE Mains 2020 MCQ

A galvanometer having a coil resistance 100 $\Omega $ gives a full scale deflection when a current of 1 mA is passed through it. What is the value of the resistance which can convert this galvanometer into a voltmeter giving full scale deflection for a potential difference of 10 V?

A

8.9 k$\Omega $

B

10 k$\Omega $

C

9.9 k$\Omega $

D

7.9 k$\Omega $

Question 159: Palette 159/275

JEE Mains 2020 MCQ

The length of a potentiometer wire is 1200 cm and it carries a current of 60 mA. For a cell of emf 5V and internal resistance of 20$\Omega $, the null point on it is found to be a 1000 cm. The resistance of whole wire is :

A

80$\Omega $

B

60$\Omega $

C

120$\Omega $

D

100$\Omega $

Question 160: Palette 160/275

JEE Mains 2020 MCQ

In a building there are 15 bulbs of 45 W, 15 bulbs of 100 W, 15 small fans of 10 W and 2 heaters of 1 kW. The voltage of electric main is 220 V. The minimum fuse capacity (rated value) of the building will be :

A

15 A

B

20 A

C

25 A

D

10 A

Question 161: Palette 161/275

JEE Mains 2020 MCQ

The current I₁ (in A) flowing through 1 $\Omega $ resistor in the following circuit is :

A

0.4

B

0.25

C

0.2

D

0.5

Question 162: Palette 162/275

JEE Mains 2019 MCQ

A moving coil galvanometer, having a resistance G, produces full scale deflection when a current Ig flows through it. This galvanometer can be converted into (i) an ammeter of range 0 to I₀(I₀ > I_g) by connecting a shunt resistance R_A to it and (ii) into a voltmeter of range 0 to V (V = GI₀) by connecting a series resistance R_V to it. Then,

A

${R_A}{R_V} = {G^2}$ and ${{{R_A}} \over {{R_V}}} = {{{I_g}} \over {\left( {{I_0} - {I_g}} \right)}}$

B

${R_A}{R_V} = {G^2}\left( {{{{I_g}} \over {{I_0} - {I_g}}}} \right)$ and ${{{R_A}} \over {{R_V}}} = {\left( {{{{I_0} - {I_g}} \over {{I_g}}}} \right)^2}$

C

${R_A}{R_V} = {G^2}\left( {{{{I_0} - {I_g}} \over {{I_g}}}} \right)$ and ${{{R_A}} \over {{R_V}}} = {\left( {{{{I_g}} \over {{I_0} - {I_g}}}} \right)^2}$

D

${R_A}{R_V} = {G^2}$ and ${{{R_A}} \over {{R_V}}} = {\left( {{{{I_g}} \over {{I_0} - {I_g}}}} \right)^2}$

Question 163: Palette 163/275

JEE Mains 2019 MCQ

To verify Ohm's law, a student connects the voltmeter across the battery as, shown in the figure. The measured voltage is plotted as a function of the current, and the following graph is obtained :
If V₀ is almost zero, identify the correct statement :

A

The value of the resistance R is 1.5 $\Omega $

B

The emf of the battery is l.5 V and its internal resistance is 1.5 $\Omega $

C

The emf of the battery is l.5 V and the value of R is 1.5 $\Omega $

D

The potential difference across the battery is 1.5 V when it sends a current of 1000 mA

Question 164: Palette 164/275

JEE Mains 2019 MCQ

The resistive network shown below is connected to a D.C. source of 16 V. The power consumed by the network is 4 Watt. The value of R is:

A

16 $\Omega $

B

1 $\Omega $

C

8 $\Omega $

D

6 $\Omega $

Question 165: Palette 165/275

JEE Mains 2019 MCQ

A galvanometer of resistance 100 $\Omega $ has 50 divisions on its scale and has sensitivitv of 20 $\mu $A/division. It is to be converted to a voltmeter with three ranges of 0-2V, 0-10 V and 0-20 V. The appropriate circuit to do so is

A

B

C

D

Question 166: Palette 166/275

JEE Mains 2019 MCQ

Space between two concentric conducting spheres of radii a and b (b > a) is filled with a medium of resistivity $\rho $. The resistance between the two spheres will be :

A

${\rho \over {2\pi }}\left( {{1 \over a} + {1 \over b}} \right)$

B

${\rho \over {4\pi }}\left( {{1 \over a} + {1 \over b}} \right)$

C

${\rho \over {2\pi }}\left( {{1 \over a} - {1 \over b}} \right)$

D

${\rho \over {4\pi }}\left( {{1 \over a} - {1 \over b}} \right)$

Question 167: Palette 167/275

JEE Mains 2019 MCQ

A moving coil galvanometer allows a full scale current of 10^–4 A. A series resistance of 2 M$\Omega $ is required to convert the above galvanometer into a voltmeter of range 0-5 V. Therefore the value of shunt resistance required to convert the above galvanometer into an ammeter of range 0.10 mA is :

A

200 $\Omega $

B

500 $\Omega $

C

100 $\Omega $

D

None of the options are correct

Question 168: Palette 168/275

JEE Mains 2019 MCQ

In an experiment, the resistance of a material is plotted as a function of temperature (in some range). As shown in the figure, it is a straight line. One may conclude that :

A

$R(T) = {R_0}{e^{ - {T^2}/T_0^2}}$

B

$R(T) = {{{R_0}} \over {{T^2}}}$

C

$R(T) = {R_0}{e^{ {T^2}/T_0^2}}$

D

$R(T) = {R_0}{e^{ - T_0^2/{T^2}}}$

Question 169: Palette 169/275

JEE Mains 2019 MCQ

A current of 5 A passes through a copper conductor (resistivity = 1.7 × 10^–8 $\Omega $m) of radius of cross-section 5 mm. Find the mobility of the charges if their drift velocity is 1.1 × 10^–3 m/s.

A

1.3 m²/Vs

B

1.0 m²/Vs

C

1.8 m²/Vs

D

1.5 m²/Vs

Question 170: Palette 170/275

JEE Mains 2019 MCQ

In the given circuit, an ideal voltmeter connected across the 10$\Omega $ resistance reads 2V. The internal resistance r, of each cell is:

A

1.5 $\Omega $

B

1 $\Omega $

C

0.5 $\Omega $

D

0 $\Omega $

Question 171: Palette 171/275

JEE Mains 2019 MCQ

In a meter bridge experiment, the circuit diagram and the corresponding observation table are shown in figure

SI. No.	R($\Omega $)	l(cm)
1.	1000	60
2.	100	13
3.	10	1.5
4.	1	1.0

Which of the readings is inconsistent?

A

4

B

3

C

2

D

1

Question 172: Palette 172/275

JEE Mains 2019 MCQ

The resistance of a galvanometer is 50 ohm and the maximum current which can be passed through it is 0.002 A. What resistance must be connected to it in order to convert it into an ammeter of range 0 – 0.5 A ?

A

0.02 ohm

B

0.2 ohm

C

0.002 ohm

D

0.5 ohm

Question 173: Palette 173/275

JEE Mains 2019 MCQ

A metal wire of resistance 3 $\Omega $ is elongated to make a uniform wire of double its previous length. This new wire is now bent and the ends joined to make a circle. If two points on this circle make an angle 60° at the centre, the equivalent resistance between these two points will be :-

A

5 /2 $\Omega $

B

12/5 $\Omega $

C

7/2 $\Omega $

D

5 / 3 $\Omega $

Question 174: Palette 174/275

JEE Mains 2019 MCQ

In a conductor, if the number of conduction electrons per unit volume is 8.5 × 10²⁸ m^–3 and mean free time is 25ƒs (femto second), it's approximate resistivity is :-
(m_e = 9.1 × 10^–31 kg)

A

10^–8 $\Omega $m

B

10^–7 $\Omega $m

C

10^–5 $\Omega $m

D

10^–6 $\Omega $m

Question 175: Palette 175/275

JEE Mains 2019 MCQ

A wire of resistance R is bent to form a square ABCD as shown in the figure. The effective resistance between E and C is : (E is mid-point of arm CD)

A

${7 \over {64}}R$

B

${1 \over {16}}R$

C

R

D

${3 \over {4}}R$

Question 176: Palette 176/275

JEE Mains 2019 MCQ

A moving coil galvanometer has resistance 50$\Omega $ and it indicates full deflection at 4mA current. A voltmeter is made using this galvanometer and a 5 k$\Omega $ resistance. The maximum voltage, that can be measured using this voltmeter, will be close to :

A

15 V

B

10 V

C

40 V

D

20 V

Question 177: Palette 177/275

JEE Mains 2019 MCQ

In the figure shown, what is the current (in Ampere) drawn from the battery ?
You are given: R₁ = 15$\Omega $, R₂ = 10 $\Omega $, R₃ = 20 $\Omega $, R₄ = 5$\Omega $, R₅ = 25$\Omega $, R₆ = 30 $\Omega $, E = 15 V

A

13/24

B

7/18

C

9/32

D

20/3

Question 178: Palette 178/275

JEE Mains 2019 MCQ

In the circuit shown, a four-wire potentiometer is made of a 400 cm long wire, which extends between A and B. The resistance per unit length of the potentiometer wire is r = 0.01 $\Omega $/cm. If an ideal voltmeter is connected as shown with jockey J at 50 cm from end A, the expected reading of the voltmeter will be :-

A

0.25 V

B

0.20 V

C

0.50V

D

0.75 V

Question 179: Palette 179/275

JEE Mains 2019 MCQ

A cell of internal resistance r drives current through an external resistance R. The power delivered by the cell to the external resistance will be maximum when :-

A

R = 1000 r

B

R = r

C

R = 2r

D

R = 0.001 r

Question 180: Palette 180/275

JEE Mains 2019 MCQ

For the circuit shown, with R₁ = 1.0W, R₂ = 2.0 W, E₁ = 2 V and E₂ = E₃ = 4 V, the potential difference between the points 'a' and 'b' is approximately (in V):

A

3.3

B

2.7

C

2.3

D

3.7

Question 181: Palette 181/275

JEE Mains 2019 MCQ

A 200 $\Omega $ resistor has a certain color code. If one replaces the red color by green in the code, the new resistance will be :

A

500 $\Omega $

B

100 $\Omega $

C

200 $\Omega $

D

300 $\Omega $

Question 182: Palette 182/275

JEE Mains 2019 MCQ

In the given circuit diagram, the currents, I₁ = – 0.3 A, I₄ = 0.8 A and I₅ = 0.4 A, are flowing as shown. The currents I₂, I₃ and I₆, respectively, are :

A

1.1 A, – 0.4 A, 0.4 A

B

$-$ 0.4 A, 0.4 A, 1.1 A

C

0.4 A, 1.1 A, 0.4 A

D

1.1 A, 0.4 A, 0.4 A

Question 183: Palette 183/275

JEE Mains 2019 MCQ

A galvanometer, whose resistance is 50 ohm, has 25 divisions in it. When a current of 4 $ \times $ 10^–4 A passes through it, its needle ( pointer) deflects by one division. To use this galvanometer as a voltmeter of range 2.5 V, it should be connected to a resistance of :

A

200 ohm

B

250 ohm

C

6200 ohm

D

6250 ohm

Question 184: Palette 184/275

JEE Mains 2019 MCQ

Two electric bulbs, rated at (25 W, 220 V) and (100 W, 220 V), are connected in series across a 220 V voltage source. If the 25 W and 100 W bulbs draw powers P₁ and P₂ respectively, then :

A

P₁ = 4W, P₂ = 16 W

B

P₁ = 16W, P₂ = 4 W

C

P₁ = 9W, P₂ = 16 W

D

P₁ = 16W, P₂ = 9 W

Question 185: Palette 185/275

JEE Mains 2019 MCQ

In a meter bridge, the wire of length 1 m has a non-uniform cross-section such that, the variation ${{dR} \over {d\ell }}$ of its resistance R with length $\ell $ is ${{dR} \over {d\ell }}$ $ \propto $ ${1 \over {\sqrt \ell }}$. Two equal resistances are connected as shown in the figure. The galvanometer has zero deflection when the jockey is at point P. What is the length AP ?

A

0.3 m

B

0.25 m

C

0.35 m

D

0.2 m

Question 186: Palette 186/275

JEE Mains 2019 MCQ

The galvanometer deflection, when key K₁ is closed but K₂ is open, equals $\theta $₀ (see figure). On closing K₂ also and adjusting R₂ to 5$\Omega $, the deflection in galvanometer becomes ${{{\theta _0}} \over 5}.$ . The resistance of the galvanometer is, then, given by [Neglect the internal resistance of battery] :

A

5 $\Omega $

B

25 $\Omega $

C

12 $\Omega $

D

22 $\Omega $

Question 187: Palette 187/275

JEE Mains 2019 MCQ

An ideal battery of 4 V and resistance R are connected in series in the primary circuit of a potentiometer of length 1 m and esistance 5 $\Omega $. The value of R, to give a potential difference of 5 mV across 10 cm of potentiometer wire, is :

A

480 $\Omega $

B

495 $\Omega $

C

490 $\Omega $

D

395 $\Omega $

Question 188: Palette 188/275

JEE Mains 2019 MCQ

A galvanometer having a resistance of 20 $\Omega $ and 30 divisions on both sides has figure of merit 0.005 ampere/division. The resistance that should be connected in series such that it can be used as a voltmeter upto 15 volt, is:

A

120 $\Omega $

B

125 $\Omega $

C

80 $\Omega $

D

100 $\Omega $

Question 189: Palette 189/275

JEE Mains 2019 MCQ

In the experimental set up of metre bridge shown in the figure, the null point is obtained at a distance of 40 cm from A. If a 10 $\Omega $ resistor is connected in series with R₁, the null point shifts by 10 cm. The resistance that should be connected in parallel with (R₁ + 10) $\Omega $ such that the null point shifts back to its initial position is :

A

40 $\Omega $

B

30 $\Omega $

C

20 $\Omega $

D

60 $\Omega $

Question 190: Palette 190/275

JEE Mains 2019 MCQ

In the circuit shown, the potential difference between A and B is :

A

6 V

B

3 V

C

2 V

D

1 V

Question 191: Palette 191/275

JEE Mains 2019 MCQ

Two equal resistances when connected in series to a battery, consume electric power of 60 W. If these resistances are now connected in parallel combination to the same battery, the electric power consumed will be :

A

240 W

B

60 W

C

30 W

D

120 W

Question 192: Palette 192/275

JEE Mains 2019 MCQ

The resistance of the meter bridge AB in given figure is 4 $\Omega $. With a cell of emf $\varepsilon $ = 0.5 V and rheostat resistance R_h = 2 $\Omega $ the null point is obtained at some point J. When the cell is replaced by another one of emf $\varepsilon $ = $\varepsilon $₂ the same null point J is found for R_h = 6 $\Omega $. The emf $\varepsilon $₂ is, :

A

0.3 V

B

0.6 V

C

0.5 V

D

0.4 V

Question 193: Palette 193/275

JEE Mains 2019 MCQ

In a Wheatstone bridge(see fig.), Resistances P and Q are approximately equal. When R = 400 $\Omega $, the bridge is balanced. On interchanging P and Q, the value of R, for balance, is 405 $\Omega $. The value of X is close to :

A

402.5 ohm

B

401.5 ohm

C

403.5 ohm

D

404.5 ohm

Question 194: Palette 194/275

JEE Mains 2019 MCQ

A current of 2 mA was passed through an unknown resistor which dissipated a power of 4.4 W. Dissipated power when an ideal power supply of 11 V is connected across it is -

A

11 $ \times $ 10^–5 W

B

11 $ \times $ 10^–3 W

C

11 $ \times $ 10⁵ W

D

11 $ \times $ 10^–4 W

Question 195: Palette 195/275

JEE Mains 2019 MCQ

The actual value of resistance R, shown in the figure is 30$\Omega $. This is measuered in an experiment as shown using the standard formula R = ${V \over {\rm I}}$, where V and I are the readings of the voltmeter and ammeter, respectively. If the measured value of R is 5% less, then the internal resistance of the voltmeter is -

A

570 $\Omega $

B

600 $\Omega $

C

350 $\Omega $

D

35 $\Omega $

Question 196: Palette 196/275

JEE Mains 2019 MCQ

The Wheatstone bridge shown in figure, here, gets balanced when the carbon resistor used as R₁ has the colour code (Orange, Red, Brown). The resistors R₂ and R₄ are 80$\Omega $ and 40$\Omega $, respectively. Assuming that the colour code for the carbon resistors gives their accurate values, the colour code for the carbon resistor, used as R₃, would be -

A

Brown, Blue, Brown

B

Grey, Black, Brown

C

Red, Green, Brown

D

Brown, Blue, Black

Question 197: Palette 197/275

JEE Mains 2019 MCQ

A 2 W carbon resistor is color coded with green, black, red and brown respectively. The maximum current which can be passed through this resistor is -

A

0.4 mA

B

20 mA

C

63 mA

D

100 mA

Question 198: Palette 198/275

JEE Mains 2019 MCQ

In the given circuit the cells have zero internal resistance. The currents (in Amperes) passing through resistance R₁ and R₂ respectively, are -

A

0.5, 0

B

0, 1

C

1, 2

D

2, 2

Question 199: Palette 199/275

JEE Mains 2019 MCQ

A potentiometer wire AB having length L and resistance 12 r is joined to a cell D of emf $\varepsilon $ and internal resistance r. A cell C having emf $\varepsilon $/2 and internal resistance 3r is connected. The length AJ at which the galvanometer as shown in figure shows no deflection is –

A

${{11} \over {12}}L$

B

${{13} \over {24}}L$

C

${{5} \over {12}}L$

D

${{11} \over {24}}L$

Question 200: Palette 200/275

JEE Mains 2019 MCQ

A uniform metallic wire has a resistance of 18 $\Omega $ and is bent into an equilateral triangle. Then, the resistance between any two vertices of the triangle is -

A

12 $\Omega $

B

2 $\Omega $

C

4 $\Omega $

D

8 $\Omega $

Question 201: Palette 201/275

JEE Mains 2019 MCQ

A carbon resistance has a following colour code. What is the value of the resistance ?

A

530 k$\Omega $ $ \pm $ 5%

B

5.3 M$\Omega $ $ \pm $ 5%

C

6.4 M$\Omega $ $ \pm $ 5%

D

64 k$\Omega $ $ \pm $ 10%

Question 202: Palette 202/275

JEE Mains 2019 MCQ

In the given circuit the the internal resistance of the 18 V cell is negligible. If R₁ = 400 $\Omega $, R₃ = 100 $\Omega $ and R₄ = 500 $\Omega $ and the reading of an ideal voltmeter across R₄ is 5V, then the value of R₂ will be :

A

300 $\Omega $

B

450 $\Omega $

C

550 $\Omega $

D

230 $\Omega $

Question 203: Palette 203/275

JEE Mains 2019 MCQ

When the switch S, in the circuit shown, is closed, then the value of current i will be :

A

3A

B

5A

C

4A

D

2A

Question 204: Palette 204/275

JEE Mains 2019 MCQ

Drift speed of electrons, when 1.5 A of current flows in a copper wire of cross section 5 mm², is $\upsilon $. If the electron density in copper is 9 $ \times $ 10²⁸/m³ the value of $\upsilon $. in mm/s is close to (Take charge of electron to be = 1.6 $ \times $ 10^$-$19C)

A

0.02

B

3

C

2

D

0.2

Question 205: Palette 205/275

JEE Mains 2019 MCQ

A resistance is shown in the figure. Its value and tolerance are given respectively by :

A

270 $\Omega $, 10 %

B

27 k$\Omega $, 10 %

C

27 k$\Omega $, 20 %

D

270 $\Omega $, 5 %

Question 206: Palette 206/275

JEE Mains 2018 MCQ

A galvanometer with its coil resistance 25 $\Omega $ requires a current of 1 mA for its full deflection. In order to construct an ammeter to read upto a current of 2 A, the approximate value of the shunt resistance should be :

A

$2.5 \times {10^{ - 3}}\,\Omega $

B

$1.25 \times {10^{ - 2}}\Omega $

C

$1.25 \times {10^{ - 3}}\Omega $

D

$2.5 \times {10^{ - 2}}\Omega $

Question 207: Palette 207/275

JEE Mains 2018 MCQ

In a circuit for finding the resistance of a galvanometer by half deflection method, a 6 V battery and a high resistance of 11 k$\Omega $ are used. The figure of merit of the galvanometer is 60 $\mu A/$division. In the absence of shunt resistance, the galvanometer produces a deflection of $\theta $ = 9 divisions when current flows in the circuit. The value of the shunt resistance that can cause the deflection of $\theta /2,$ is closest to :

A

500 $\Omega $

B

220 $\Omega $

C

55 $\Omega $

D

110 $\Omega $

Question 208: Palette 208/275

JEE Mains 2018 MCQ

A heating element has a resistance of 100 $\Omega $ at room temperature. When it is connected to a supply of 220 V, a steady current of 2 A passes in it and temperature is 500^oC more than room temperature. what is the temperature coefficient of resistance of the heating element ?

A

0.5 $ \times $ 10^{$-$4 o}C^$-$1

B

5 $ \times $ 10^{$-$4 o}C^$-$1

C

1 $ \times $ 10^{$-$4 o}C^$-$1

D

2 $ \times $ 10^{$-$4 o}C^$-$1

Question 209: Palette 209/275

JEE Mains 2018 MCQ

Two batteries with e.m.f 12 V and 13 V are connected in parallel across a load resistor of 10 $\Omega $. The internal resistances of the two batteries are 1 $\Omega $ and 2 $\Omega $ respectively. The voltage across the load lies between :

A

11.7 V and 11.8 V

B

11.6 V and 11.7 V

C

11.5 V and 11.6 V

D

11.4 V and 11.5 V

Question 210: Palette 210/275

JEE Mains 2018 MCQ

On interchanging the resistances, the balance point of a meter bridge shifts to the left by 10 cm. The resistance of their series combination is 1 k$\Omega $. How much was the resistance on the left slot before interchanging the resistances?

A

910 $\Omega $

B

990 $\Omega $

C

505 $\Omega $

D

550 $\Omega $

Question 211: Palette 211/275

JEE Mains 2018 MCQ

In a potentiometer experiment, it is found that no current passes through the galvanometer when the terminals of the cell are connected across 52 cm of the potentiometer wire. If the cell is shunted by a resistance of 5 $\Omega$, a balance is found when the cell is connected across 40 cm of the wire. Find the internal resistance of the cell.

A

2.5 $\Omega$

B

1 $\Omega$

C

1.5 $\Omega$

D

2 $\Omega$

Question 212: Palette 212/275

JEE Mains 2018 MCQ

A copper rod of cross-sectional area A carries a uniform current I through it. At temperature T, if the volume charge density of the rod is $\rho $, how long will the changes take to travel a distance d ?

A

${{2\rho \,d\,A} \over {\rm I}}$

B

${{2\rho \,d\,A} \over {{\rm I}\,T}}$

C

${{\rho \,d\,A} \over {{\rm I}\,}}$

D

${{\rho \,d\,A} \over {{\rm I}\,T}}$

Question 213: Palette 213/275

JEE Mains 2018 MCQ

A constant voltages is applied between two ends of a metallic wire. If the length is halved and the radius of the wire is doubled, the rate of heat developed in the wire will be :

A

Doubled

B

Halved

C

Unchanged

D

Increased 8 times

Question 214: Palette 214/275

JEE Mains 2018 MCQ

In the given circuit all resistances are of value $R$ $ohm$ each. The equivalent resistance between $A$ and $B$ is :

A

$2R$

B

$3R$

C

${{5R} \over 3}$

D

${{5R} \over 2}$

Question 215: Palette 215/275

JEE Mains 2018 MCQ

In a meter bridge, as shown in the figure, it is given that resistance $Y = 12.5\,\,\Omega $ and that the balance is obtained at a distance $39.5$ $cm$ from end $A$ (by Jockey J). After interchanging the resistances $X$ and $Y$, a new balance point is found at a distance ${l_2}$ from end $A.$ What are the value of $X$ and ${l_2}$ ?

A

$8.16\,\,\Omega $ and $60.5$ $cm$

B

$19.15\,\,\Omega $ and $39.5$ $cm$

C

$8.16\,\,\Omega $ and $39.5$ $cm$

D

$19.15\,\,\Omega $ and $60.5$ $cm$

Question 216: Palette 216/275

JEE Mains 2017 MCQ

The figure shows three circuits I, II and III which are connected to a 3V battery. If the powers dissipated by the configurations I, II and III are P₁ , P₂ and P₃ respectively, then :

A

P₁ > P₂ > P₃

B

P₁ > P₃ > P₂

C

P₂ > P₁ > P₃

D

P₃ > P₂ > P₁

Question 217: Palette 217/275

JEE Mains 2017 MCQ

In a meter bridge experiment resistances are connected as shown in the figure. Initially resistance P = 4 $\Omega $ and the neutral point N is at 60 cm from A. Now an unknown resistance R is connected in series to P and the new position of the neutral point is at 80 cm from A. The value of unknown resistance R is :

A

${{33} \over 5}\,\Omega $

B

6 $\,\Omega $

C

7 $\,\Omega $

D

${{20} \over 3}\,\Omega $

Question 218: Palette 218/275

JEE Mains 2017 MCQ

A uniform wire of length 1 and radius r has a resistance of 100 $\Omega $. It is recast into a wire of radius ${r \over 2}.$ The resistance of new wire will be :

A

1600 $\Omega $

B

400 $\Omega $

C

200 $\Omega $

D

100 $\Omega $

Question 219: Palette 219/275

JEE Mains 2017 MCQ

A 9 V battery with internal resistance of 0.5 $\Omega $ is connected across an infinite network as shown in the figure. All ammeters A₁, A₂, ₃ and voltmeter V are ideal.
Choose correct statement.

A

Reading of A₁ is 2 A

B

Reading of A₁ is 18 A

C

Reading of   V   is  9 V

D

Reading of   V   is   7 V

Question 220: Palette 220/275

JEE Mains 2017 MCQ

A potentiometer PQ is set up to compare two resistances as shown in the figure. The ammeter A in the circuit reads 1.0 A when two way key K₃ is open. The balance point is at a length $\ell $₁ cm from P when two way key K₃ is plugged in between 2 and 1, while the balance point is at a length $\ell $₂ cm from P when key K₃ is plugged in between 3 and 1. The ratio of two resistances ${{{R_1}} \over {{R_2}}}$, is found to be :

A

${{{l_1}} \over {{l_1} + {l_2}}}$

B

${{{l_2}} \over {{l_2} - {l_1}}}$

C

${{{l_1}} \over {{l_1} - {l_2}}}$

D

${{{l_1}} \over {{l_2} - {l_1}}}$

Question 221: Palette 221/275

JEE Mains 2017 MCQ

When a current of 5 mA is passed through a galvanometer having a coil of resistance 15$\Omega $, it shows full scale deflection. The value of the resistance to be put in series with the galvanometer to convert it into a voltmeter of range 0 – 10V is:

A

4.005 × 10³ $\Omega $

B

1.985 × 10³ $\Omega $

C

2.535 × 10³ $\Omega $

D

2.045 × 10³ $\Omega $

Question 222: Palette 222/275

JEE Mains 2017 MCQ

Which of the following statements is false?

A

Kirchhoff’s second law represents energy conservation.

B

Wheatstone bridge is the most sensitive when all the four resistances are of the same order of magnitude.

C

In a balanced wheatstone bridge if the cell and the galvanometer are exchanged, the null point is disturbed.

D

A rheostat can be used as a potential divider.

Question 223: Palette 223/275

JEE Mains 2017 MCQ

In the given circuit, the current in each resistance is:

A

0 A

B

1 A

C

0.25 A

D

0.5 A

Question 224: Palette 224/275

JEE Mains 2016 MCQ

The resistance of an electrical toaster has a temperature dependence given by R(T) = R₀ [1 + $\alpha $(T − T₀)] in its range of operation. At T₀ = 300 K, R = 100 $\Omega $ and at T = 500 K, R = 120 $\Omega $. The toaster is connected to a voltage source at 200 V and its temperature is raised at a constant rate from 300 to 500 K in 30 s. The total work done in raising the temperature is :

A

400 $\ln \,{{1.5} \over {1.3}}\,J$

B

200 $\ln \,{{2} \over {3}}\,J$

C

60000 $\ln \,{{6} \over {5}}\,J$

D

300 J

Question 225: Palette 225/275

JEE Mains 2016 MCQ

A galvanometer has a 50 division scale. Battery has no internal resistance. It is found that there is deflection of 40 divisions when R = 2400 $\Omega $. Deflection becomes 20 divisions when resistance taken from resistance box is 4900 $\Omega $. Then we can conclude :

A

Resistance of galvanometer is 200 $\Omega $

B

Full scale deflection current is 2 mA.

C

Current sensitivity of galvanometer is 20 $\mu $A/division.

D

Resistance required on R.B. for a deflection of 10 divisions is 9800 $\Omega $.

Question 226: Palette 226/275

JEE Mains 2016 MCQ

In the circuit shown, the resistance r is a variable resistance. If for r = fR, the heat generation in r is maximum then the value of f is :

A

${1 \over 4}$

B

${1 \over 2}$

C

${3 \over 4}$

D

1

Question 227: Palette 227/275

JEE Mains 2016 MCQ

A 50 $\Omega $ resistance is connected to a battery of 5 V. A galvanometer of resistance 100 $\Omega $ is to be used as an ammeter to measure current through the resistance, for this a resistance r_s is connected to the galvanometer. Which of the following connections should be employed if the measured current is within 1% of thecurrent without the ammeter in the circuit ?

A

r_s = 0.5 $\Omega $ in parallel with the galvanometer

B

r_s = 0.5 $\Omega $ in series with the galvanometer

C

r_s = 1 $\Omega $ in series with galvanometer

D

r_s =1 $\Omega $ in parallel with galvanometer

Question 228: Palette 228/275

JEE Mains 2016 MCQ

A galvanometer having a coil resistance of $100\,\Omega $ gives a full scale deflection, when a currect of $1$ $mA$ is passed through it. The value of the resistance, which can convert this galvanometer into ammeter giving a full scale deflection for a current of $10$ $A,$ is :

A

$0.1\,\Omega $

B

$3\,\Omega $

C

$0.01\,\Omega $

D

$2\,\Omega $

Question 229: Palette 229/275

JEE Mains 2015 MCQ

When $5V$ potential difference is applied across a wire of length $0.1$ $m,$ the drift speed of electrons is $2.5 \times {10^{ - 4}}\,\,m{s^{ - 1}}.$ If the electron density in the wire is $8 \times {10^{28}}\,\,{m^{ - 3}},$ the resistivity of the material is close to :

A

$1.6 \times {10^{ - 6}}\Omega m$

B

$1.6 \times {10^{ - 5}}\Omega m$

C

$1.6 \times {10^{ - 8}}\Omega m$

D

$1.6 \times {10^{ - 7}}\Omega m$

Question 230: Palette 230/275

JEE Mains 2015 MCQ

In the circuit shown, the current in the $1\Omega $ resistor is :

A

$0.13$ $A,$ from $Q$ to $P$

B

$0.13$ $A$, from $P$ to $Q$

C

$1.3A$ from $P$ to $Q$

D

$0A$

Question 231: Palette 231/275

JEE Mains 2014 MCQ

In a large building, three are $15$ bulbs of $40$ $W$, $5$ bulbs of $100$ $W$, $5$ fans of $80$ $W$ and $1$ heater of $1$ $kW.$ The voltage of electric mains is $220$ $V.$ The minimum capacity of the main fuse of the building will be:

A

$8$ $A$

B

$10$ $A$

C

$12$ $A$

D

$14$ $A$

Question 232: Palette 232/275

JEE Mains 2013 MCQ

This questions has Statement - ${\rm I}$ and Statement - ${\rm I}$${\rm I}$. Of the four choices given after the Statements, choose the one that best describes into two Statements.

Statement - ${\rm I}$ : Higher the range, greater is the resistance of ammeter.
Statement - ${\rm I}$${\rm I}$ : To increase the range of ammeter, additional shunt needs to be used across it.

A

Statement - ${\rm I}$ is true, Statement - ${\rm II}$ is true, Statement - ${\rm II}$ is the correct explanation of statement - ${\rm I}$.

B

Statement - ${\rm I}$ is true, Statement - ${\rm II}$ is true, Statement - ${\rm II}$ is not the correct explanation of statement - ${\rm I}$.

C

Statement - ${\rm I}$ is true, Statement - ${\rm II}$ is false

D

Statement - ${\rm I}$ is false, Statement - ${\rm II}$ is true

Question 233: Palette 233/275

JEE Mains 2013 MCQ

The supply voltage to room is $120V.$ The resistance of the lead wires is $6\Omega $. A $60$ $W$ bulb is already switched on. What is the decrease of voltage across the bulb, when a $240$ $W$ heater is switched on in parallel to the bulb?

A

zero

B

$2.9$ Volt

C

$13.3$ Volt

D

$10.04$ Volt

Question 234: Palette 234/275

JEE Mains 2012 MCQ

Two electric bulbs marked $25W$ $-$ $220$ $V$ and $100W$ $-$ $220V$ are connected in series to a $440$ $V$ supply. Which of the bulbs will fuse?

A

Both

B

$100$ $W$

C

$25$ $W$

D

Neither

Question 235: Palette 235/275

JEE Mains 2011 MCQ

If a wire is stretched to make it $0.1\% $ longer, its resistance will:

A

increase by $0.2\% $

B

decrease by $0.2\% $

C

decrease by $0.05\% $

D

increase by $0.05\% $

Question 236: Palette 236/275

JEE Mains 2010 MCQ

Two conductors have the same resistance at ${0^ \circ }C$ but their temperature coefficients of resistance are ${\alpha _1}$ and ${\alpha _2}.$ The respective temperature coefficients of their series and parallel combinations are nearly

A

${{{\alpha _1} + {\alpha _2}} \over 2},\,{\alpha _1} + {\alpha _2}$

B

${\alpha _1} + {\alpha _2},\,{{{\alpha _1} + {\alpha _2}} \over 2}$

C

${\alpha _1} + {\alpha _2},\,{{{\alpha _1}{\alpha _2}} \over {{\alpha _1} + {\alpha _2}}}$

D

${{{\alpha _1} + {\alpha _2}} \over 2},\,{{{\alpha _1} + {\alpha _2}} \over 2}$

Question 237: Palette 237/275

JEE Mains 2008 MCQ

Consider a block of conducting material of resistivity $'\rho '$ shown in the figure. Current $'I'$ enters at $'A'$ and leaves from $'D'$. We apply superposition principle to find voltage $'\Delta V'$ developed between $'B'$ and $'C'$. The calculation is done in the following steps:
(i) Take current $'I'$ entering from $'A'$ and assume it to spread over a hemispherical surface in the block.
(ii) Calculate field $E(r)$ at distance $'r'$ from A by using Ohm's law $E = \rho j,$ where $j$ is the current per unit area at $'r'$.
(iii) From the $'r'$ dependence of $E(r)$, obtain the potential $V(r)$ at $r$.
(iv) Repeat (i), (ii) and (iii) for current $'I'$ leaving $'D'$ and superpose results for $'A'$ and $'D'.$

For current entering at $A,$ the electric field at a distance $'r'$ from $A$ is

A

${{\rho I} \over {8\pi {r^2}}}$

B

${{\rho I} \over {{r^2}}}$

C

${{\rho I} \over {2\pi {r^2}}}$

D

${{\rho I} \over {4\pi {r^2}}}$

Question 238: Palette 238/275

JEE Mains 2008 MCQ

Shown in the figure below is a meter-bridge set up with null deflection in the galvanometer.

The value of the unknown resister $R$ is

A

$13.75\Omega $

B

$220\Omega $

C

$110\Omega $

D

$55\Omega $

Question 239: Palette 239/275

JEE Mains 2008 MCQ

A $5V$ battery with internal resistance $2\Omega $ and a $2V$ battery with internal resistance $1\Omega $ are connected to a $10\Omega $ resistor as shown in the figure.

The current in the $10\Omega $ resistor is

A

$0.27A{P_2}\,\,to\,\,{P_1}$

B

$0.03A{P_1}\,\,to\,\,{P_2}$

C

$0.03A{P_2}\,\,to\,\,{P_1}$

D

$0.27A{P_1}\,\,to\,\,{P_2}$

Question 240: Palette 240/275

JEE Mains 2008 MCQ

Consider a block of conducting material of resistivity $'\rho '$ shown in the figure. Current $'I'$ enters at $'A'$ and leaves from $'D'$. We apply superposition principle to find voltage $'\Delta V'$ developed between $'B'$ and $'C'$. The calculation is done in the following steps:
(i) Take current $'I'$ entering from $'A'$ and assume it to spread over a hemispherical surface in the block.
(ii) Calculate field $E(r)$ at distance $'r'$ from A by using Ohm's law $E = \rho j,$ where $j$ is the current per unit area at $'r'$.
(iii) From the $'r'$ dependence of $E(r)$, obtain the potential $V(r)$ at $r$.
(iv) Repeat (i), (ii) and (iii) for current $'I'$ leaving $'D'$ and superpose results for $'A'$ and $'D'.$

$\Delta V$ measured between $B$ and $C$ is

A

${{\rho I} \over {\pi a}} - {{\rho I} \over {\pi \left( {a + b} \right)}}$

B

${{\rho I} \over a} - {{\rho I} \over {\left( {a + b} \right)}}$

C

${{\rho I} \over {2\pi a}} - {{\rho I} \over {2\pi \left( {a + b} \right)}}$

D

${{\rho I} \over {2\pi \left( {a - b} \right)}}$

Question 241: Palette 241/275

JEE Mains 2007 MCQ

The resistance of a wire is $5$ ohm at ${50^ \circ }C$ and $6$ ohm at ${100^ \circ }C.$ The resistance of the wire at ${0^ \circ }C$ will be

A

$3$ ohm

B

$2$ ohm

C

$1$ ohm

D

$4$ ohm

Question 242: Palette 242/275

JEE Mains 2006 MCQ

The resistance of bulb filmanet is $100\Omega $ at a temperature of ${100^ \circ }C.$ If its temperature coefficient of resistance be $0.005$ per $^ \circ C$, its resistance will become $200\,\Omega $ at a temperature of

A

${300^ \circ }C$

B

${400^ \circ }C$

C

${500^ \circ }C$

D

${200^ \circ }C$

Question 243: Palette 243/275

JEE Mains 2006 MCQ

In a Wheatstone's bridge, three resistance $P, Q$ and $R$ connected in the three arms and the fourth arm is formed by two resistances ${S_1}$ and ${S_2}$ connected in parallel. The condition for the bridge to be balanced will be

A

${P \over Q} = {{2R} \over {{S_1} + {S_2}}}$

B

${P \over Q} = {{R\left( {{S_1} + {S_2}} \right)} \over {{S_1}{S_2}}}$

C

${P \over Q} = {{R\left( {{S_1} + {S_2}} \right)} \over {2{S_1}{S_2}}}$

D

${P \over Q} = {R \over {{S_1} + {S_2}}}$

Question 244: Palette 244/275

JEE Mains 2006 MCQ

A thermocouple is made from two metals, Antimony and Bismuth. If one junction of the couple is kept hot and the other is kept cold, then, an electric current will

A

flow from Antimony to Bismuth at the hot junction

B

flow from Bismuth to Antimony at the cold junction

C

now flow through the thermocouple

D

flow from Antimony to Bismuth at the cold junction

Question 245: Palette 245/275

JEE Mains 2006 MCQ

An electric bulb is rated $220$ volt - $100$ watt. The power consumed by it when operated on $110$ volt will be

A

$75$ watt

B

$40$ watt

C

$25$ Watt

D

$50$ Watt

Question 246: Palette 246/275

JEE Mains 2006 MCQ

The current ${\rm I}$ drawn from the $5$ volt source will be

A

$0.33$ $A$

B

$0.5$ $A$

C

$0.67$ $A$

D

$0.17$ $A$

Question 247: Palette 247/275

JEE Mains 2005 MCQ

Two sources of equal $emf$ are connected to an external resistance $R.$ The internal resistance of the two sources are ${R_1}$ and ${R_2}\left( {{R_1} > {R_1}} \right).$ If the potential difference across the source having internal resistance ${R_2}$ is zero, then

A

$R = {R_2} - {R_1}$

B

$R = {R_2} \times \left( {{R_1} + {R_2}} \right)/\left( {{R_2} - {R_1}} \right)$

C

$R = {R_1}{R_2}/\left( {{R_2} - {R_1}} \right)$

D

$R = {R_1}{R_2}/\left( {{R_1} - {R_2}} \right)$

Question 248: Palette 248/275

JEE Mains 2005 MCQ

An energy source will supply a constant current into the load if its internal resistance is

A

very large as compared to the load resistance

B

equal to the resistance of the load

C

non-zero but less than the resistance of the load

D

zero

Question 249: Palette 249/275

JEE Mains 2005 MCQ

A moving coil galvanometer has $150$ equal divisions. Its current sensitivity is $10$- divisions per milliampere and voltage sensitivity is $2$ divisions per millivolt. In order that each division reads $1$ volt, the resistance in $ohms$ needed to be connected in series with the coil will be -

A

${10^5}$

B

${10^3}$

C

$9995$

D

$99995$

Question 250: Palette 250/275

JEE Mains 2005 MCQ

In the circuit, the galvanometer $G$ shows zero deflection. If the batteries $A$ and $B$ have negligible internal resistance, the value of the resistor $R$ will be -

A

$100\Omega $

B

$200\Omega $

C

$1000\Omega $

D

$500\Omega $

Question 251: Palette 251/275

JEE Mains 2005 MCQ

Two voltmeters, one of copper and another of silver, are joined in parallel. When a total charge $q$ flows through the voltmeters, equal amount of metals are deposited. If the electrochemical equivalents of copper and silver are ${Z_1}$ and ${Z_2}$ respectively the charge which flows through the silver voltmeter is

A

${q \over {1 + {{{Z_2}} \over {{Z_1}}}}}$

B

${q \over {1 + {{{Z_1}} \over {{Z_2}}}}}$

C

$q{{{Z_2}} \over {{Z_1}}}$

D

$q{{{Z_1}} \over {{Z_2}}}$

Question 252: Palette 252/275

JEE Mains 2005 MCQ

A heater coil is cut into two equal parts and only one part is now used in the heater. The heat generated will now be

A

four times

B

doubled

C

halved

D

one fourth

Question 253: Palette 253/275

JEE Mains 2005 MCQ

In a potentiometer experiment the balancing with a cell is at length $240$ $cm.$ On shunting the cell with a resistance of $2\Omega ,$ the balancing length becomes $120$ $cm$. The internal resistance of the cell is

A

$0.5\Omega $

B

$1\Omega $

C

$2\Omega $

D

$4\Omega $

Question 254: Palette 254/275

JEE Mains 2005 MCQ

The resistance of hot tungsten filament is about $10$ times the cold resistance. What will be resistance of $100$ $W$ and $200$ $V$ lamp when not in use ?

A

$20\Omega $

B

$40\Omega $

C

$200\Omega $

D

$400\Omega $

Question 255: Palette 255/275

JEE Mains 2004 MCQ

The thermo $emf$ of a thermocouple varies with temperature $\theta $ of the hot junction as $E = a\theta + b{\theta ^2}$ in volts where the ratio $a/b$ is ${700^ \circ }C.$ If the cold junction is kept at ${0^ \circ }C,$ then the neutral temperature is

A

${1400^ \circ }C$

B

${350^ \circ }C$

C

${700^ \circ }C$

D

No neutral temperature is possible for this termocouple.

Question 256: Palette 256/275

JEE Mains 2004 MCQ

An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the lengths and radii are in the ratio of ${4 \over 3}$ and ${2 \over 3}$, then the ratio of the current passing through the wires will be

A

$8/9$

B

$1/3$

C

$3$

D

$2$

Question 257: Palette 257/275

JEE Mains 2004 MCQ

The Kirchhoff's first law $\left( {\sum i = 0} \right)$ and second law $\left( {\sum iR = \sum E} \right),$ where the symbols have their usual meanings, are respectively based on

A

conservation of charge, conservation of momentum

B

conservation of energy, conservation of charge

C

conservation of momentum, conservation of charge

D

conservation of charge, conservation of energy

Question 258: Palette 258/275

JEE Mains 2004 MCQ

Thermistors are usually made of

A

metal oxides with high temperature coefficient of resistivity

B

metals with high temperature coefficient of resistivity

C

metals with low temperature coefficient of resistivity

D

semiconducting materials having low temperature

Question 259: Palette 259/275

JEE Mains 2004 MCQ

In a meter bridge experiment null point is obtained at $20$ $cm$, from one end of the wire when resistance $X$ is balanced against another resistance $Y.$ If $X < Y$, then where will be the new position of the null point from the same end, if one decides to balance a resistance of $4$ $X$ against $Y$

A

$40$ $cm$

B

$80$ $cm$

C

$50$ $cm$

D

$70$ $cm$

Question 260: Palette 260/275

JEE Mains 2004 MCQ

The electrochemical equivalent of a metal is ${3.35109^{ - 7}}$ $kg$ per Coulomb. The mass of the metal liberated at the cathode when a $3A$ current is passed for $2$ seconds will be

A

$6.6 \times {10^{57}}/kg$

B

$9.9 \times {10^{ - 7}}\,kg$

C

$19.8 \times {10^{ - 7}}\,kg$

D

$1.1 \times {10^{ - 7}}\,kg$

Question 261: Palette 261/275

JEE Mains 2004 MCQ

The resistance of the series combination of two resistances is $S.$ When they are jointed in parallel the total resistance is $P.$ If $S = nP$ then the Minimum possible value of $n$ is

A

$2$

B

$3$

C

$4$

D

$1$

Question 262: Palette 262/275

JEE Mains 2004 MCQ

A material $'B'$ has twice the specific resistance of $'A'.$ A circular wire made of $'B'$ has twice the diameter of a wire made of $'A'$. Then for the two wires to have the same resistance, the ratio ${l \over B}/{l \over A}$ of their respective lengths must be

A

$1$

B

${l \over 2}$

C

${l \over 4}$

D

$2$

Question 263: Palette 263/275

JEE Mains 2004 MCQ

The total current supplied to the circuit by the battery is

A

$4A$

B

$2A$

C

$1A$

D

$6A$

Question 264: Palette 264/275

JEE Mains 2003 MCQ

A $3$ volt battery with negligible internal resistance is connected in a circuit as shown in the figure. The current ${\rm I}$, in the circuit will be

A

$1$ $A$

B

$1.5$ $A$

C

$2$ $A$

D

$1/3$ $A$

Question 265: Palette 265/275

JEE Mains 2003 MCQ

The nagative $Zn$ pole of a Daniell cell, sending a constant current through a circuit, decreases in mass by $0.13g$ in $30$ minutes. If the electrochemical equivalent of $Zn$ and $Cu$ are $32.5$ and $31.5$ respectively, the increase in the mass of the positive $Cu$ pole in this time is

A

$0.180$ $g$

B

$0.141$ $g$

C

$0.126$ $g$

D

$0.242$ $g$

Question 266: Palette 266/275

JEE Mains 2003 MCQ

A $220$ volt, $1000$ watt bulb is connected across a $110$ $volt$ mains supply. The power consumed will be

A

$750$ watt

B

$500$ watt

C

$250$ watt

D

$1000$ watt

Question 267: Palette 267/275

JEE Mains 2003 MCQ

The length of a wire of a potentiometer is $100$ $cm$, and the $e.$ $m.$ $f.$ of its standard cell is $E$ volt. It is employed to measure the $e.m.f.$ of a battery whose internal resistance in $0.5\Omega .$ If the balance point is obtained at $1=30$ $cm$ from the positive end, the $e.m.f.$ of the battery is

where $i$ is the current in the potentiometer wire.

A

${{30E} \over {100.5}}$

B

${{30E} \over {\left( {100 - 0.5} \right)}}$

C

${{30\left( {E - 0.5i} \right)} \over {100}}$

D

${{30E} \over {100}} - 0.5i$, where i is the current in the potentiometer wire

Question 268: Palette 268/275

JEE Mains 2003 MCQ

The thermo $e.m.f.$ of a thermo -couple is $25$ $\mu V/{}^ \circ C$ at room temperature. A galvanometer of $40$ $ohm$ resistance, capable of detecting current as low as ${10^{ - 5}}\,A,$ is connected with the thermo couple. The smallest temperature difference that can be detected by this system is

A

${16^0}C$

B

${12^0}C$

C

${8^0}C$

D

${20^0}C$

Question 269: Palette 269/275

JEE Mains 2003 MCQ

An ammeter reads upto $1$ ampere. Its internal resistance is $0.81$ $ohm$. To increase the range to $10$ $A$ the value of the required shunt is

A

$0.03\,\Omega $

B

$0.3\,\Omega $

C

$0.9\,\Omega $

D

$0.09\,\Omega $

Question 270: Palette 270/275

JEE Mains 2003 MCQ

The length of a given cylindrical wire is increased by $100\% $. Due to the consequent decrease in diameter the change in the resistance of the wire will be

A

$200\% $

B

$100\% $

C

$50\% $

D

$300\% $

Question 271: Palette 271/275

JEE Mains 2002 MCQ

If ${\theta _1},$ is the inversion temperature, ${\theta _n}$ is the neutral temperature, ${\theta _c}$ is the temperature of the cold junction, then

A

${\theta _i} + {\theta _c} = {\theta _n}$

B

${\theta _i} - {\theta _c} = 2{\theta _n}$

C

${{{\theta _i} + {\theta _C}} \over 2} = {\theta _n}$

D

${\theta _c} - {\theta _i} = 2{\theta _n}$

Question 272: Palette 272/275

JEE Mains 2002 MCQ

The mass of product liberated on anode in an electrochemical cell depends on (where $t$ is the time period for which the current is passed).

A

${\left( {It} \right)^{1/2}}$

B

$It$

C

$I/t$

D

${I^2}t$

Question 273: Palette 273/275

JEE Mains 2002 MCQ

If an ammeter is to be used in place of a voltmeter, then we must connect with the ammeter a

A

low resistance in parallel

B

high resistance in parallel

C

high resistance in series

D

low resistance in series

Question 274: Palette 274/275

JEE Mains 2002 MCQ

A wire when connected to $220$ $V$ mains supply has power dissipation ${P_1}.$ Now the wire is cut into two equal pieces which are connected in parallel to the same supply. Power dissipation in this case is ${P_2}.$ Then ${P_2}:{P_1}$ is

A

$1$

B

$4$

C

$2$

D

$3$

Question 275: Palette 275/275

JEE Mains 2002 MCQ

If in the circuit, power dissipation is $150W,$ then $R$ is

A

$2\,\Omega $

B

$6\,\Omega $

C

$5\,\Omega $

D

$4\,\Omega $