The area of cross-section of a potentiometer wire is $6 \times 10^{-7} \mathrm{~m}^2$. The potential difference per unit length of the potentiometer wire when it is connected to a cell of negligible internal resistance and a resistor in series is $0.15 \mathrm{Vm}^{-1}$. If the current through potentiometer wire is 0.3 A , then the resistivity of the material of the potentiometer wire is

The lengths of two wires made of the same material are in the ratio $2: 3$ and their radii are in the ratio $1: 2$. If the two wires are connected in parallel to a battery, then the ratio of the drift velocities of free electrons in the two wires is

In a potentiometer experiment for the determination of the internal resistance of a cell, when an external resistance of $R$ is connected parallel to the cell, the balancing length decreases by $10 \%$. The internal resistance of the cell is

The potential difference between the terminals of a cell is 20 V when a current of 2 A flows through the circuit. When the direction of current in the circuit is reversed, the potential difference between the terminals of the cell is 30 V . The internal resistance of the cell is

A straight uniform wire of resistance $36 \Omega$ is bent in the form of a semi-circular loop. The effective resistance between the ends of the diameter of the semi-circular loop is

The ratios of the voltage sensitivities, resistances and areas of the coils of two moving coil galvanometers $A$ and $B$ are $4: 3,3: 4$ and $1: 2$ respectively. If the number of turns of the coil of galvanometer $A$ is 200 , then the number of turns of the coil of galvanometer $B$ is (All other quantities remain same in both the cases)

The potential difference between points $C$ and $D$ of the electrical circuit shown in the figure is

The length of a potentiometer wire is 2.5 m and its resistance is $8 \Omega$. A cell of negligible internal resistance and emf of 2.5 V is connected in series with a resistance of $242 \Omega$ in the primary circuit. The potential difference between two points separated by a distance of 20 cm on the potentiometer wire is

In a potentiometer experiment, a wire of length 10 m and resistance $5 \Omega$ is connected to a cell of emf 2.2 V . If the potential difference between two points separated by a distance of 660 cm on potentiometer wire is 1.1 V , then the internal resistance of the cell is

When the right gap of a metre bridge consists of two equal resistors in series, the balancing point is at 50 cm . When one of the resisters in the right gap is removed and is connected in parallel to the resistor in the left gap, the balancing point is at

The drift speed of electrons in a material is found to be $0.3 \mathrm{~ms}^{-1}$ when an electric field of $2 \mathrm{Vm}^{-1}$ is applied across it. The electron mobility (in $\mathrm{m}^2 \mathrm{~V}^{-1} \mathrm{~s}^{-1}$ ) in the material is

The power of an electric motor is 242 W when connected to a 220 V supply. When the motor is operated at 200 V , the current drawn by it is

A conductor of length 1.5 m and area of cross-section $3 \times 10^{-5} \mathrm{~m}^2$ has electrical resistance of $15 \Omega$.

The current density in the conductor for an electric field of $21 \mathrm{Vm}^{-1}$ is

The potential difference $V$ across the filament of the bulb shown in the given Wheatstone bridge varies as $V=i(2 i+1)$, where $i$ is the current in ampere through the filament of the bulb. The emf of the battery $V_a$, so that the bridge become balanced is

Three resistors of resistances $10 \Omega, 20 \Omega$ and $30 \Omega$ are connected as shown in the figure. If the points $A, B$ and $C$ are at potentials $10 \mathrm{~V}, 6 \mathrm{~V}$ and 5 V respectively, then the ratio of the magnitudes of the currents through $10 \Omega$ and $30 \Omega$ resistors is

A uniform conducting wire $A B$ of length 5 m and resistance $5 \Omega$ is connected as shown in the circuit. If the balancing point is obtained at 3 m from $A$, then the value of $E$ is

In the given circuit, the equivalent resistance between $A$ and $B$ is

The Wheatstone bridge shown in the diagram is balanced. If $P_3$ is the power dissipated by $R_3$ and $P_1$ is the power dissipated by $R_1$, then the ratio $P_3 / P_1$ is

A wire of resistance $2 R$ is stretched such that its length is doubled. Then the increase in its resistance is

If the masses of three wires of same material are in the ratio of $1: 2: 3$ and their lengths are in the ratio of $3: 2: 1$, then electrical resistances of these wires are in the ratio

As shown in the figure, in a Wheatstone's bridge, three resistances $P, Q$ and $R$ are 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 is

The electric resistance of a certain wire of iron is $R$. If its length and radius are both doubled, then

In a meter bridge experiment the ratio of the left gap resistance to the right gap resistance is $2: 3$. The balance length from left end is

In a galvanometer, $5 \%$ of the total current in the circuit passes through it. If the resistance of the galvanometer is $G$, the shunt resistance $S$ connected to the galvanometer is

A potentiometer balances at 44 cm when a cell of internal resistance $1 \Omega$ is in the secondary circuit. To obtains the balancing point at 40 cm , the resistance to be connected parallel to cell is

Two wires made of the same material have lengths in the ratio $2: 3$ and radii in the ratio $8: 9$. If the same potential difference is applied across the ends of the wires, the ratio of the electric currents flowing through them is

Which of the following is the unit of mobility of a electron in a conductor?

The time required to raise the temperature 3 litre of water from $0^{\circ} \mathrm{C}$ to $80^{\circ} \mathrm{C}$ by a heater operated under 200 V having resistance of $50 \Omega$ is [specific heat capacity of water is $4200 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$ ] [density of water $=1000 \mathrm{~kg} / \mathrm{m}^3$ ]

The current density in a circular wire is given by $J(r)=\left(1 \times 10^5 \mathrm{~A} / \mathrm{m}^3\right) r$, where $r$ is the radial distance and the wire's radius is 2 mm . If the potential applied across the wire is 70 V , then the energy consumed by the wire in 1000 s is

Statement I Specific resistance depends on nature of material and independent of temperature of the material. Statement II A wire of resistance $6 \Omega$ is drawn out, so that its new length is four times its original length. The resistance of the new wire is $48 \Omega$.

Statement III Drift velocity is the average constant velocity acquired by free electrons inside a metal by the application of an electric field which results in current. Which of the following is correct?

Find the mobility of electron in a wire, if its average collision time is $9.1 \times 10^{-15} \mathrm{~s}$. (Charge of electron $=1.6 \times 10^{-19} \mathrm{C}$ and mass of electron $=9.1 \times 10^{-31} \mathrm{~kg}$ )

Statement I The temperature coefficient of resistance for most of metals in pure form is positive.

Statement II A metal wire 2 mm in diameter carries a charge of $360 \pi \mathrm{C}$ in two hours. If the metal contains $5 \times 10^{22}$ free electrons $/ \mathrm{cm}^3$, then drift velocity of the electrons in the wire is $6.25 \times 10^{10} \mathrm{~m} / \mathrm{s}$.

Statement III Semiconductors like pure germanium does not obey Ohm's law for all range of electric field values.

Which of the following is correct?

A cylindrical resistor of radius 7.0 mm and length 4.0 cm is made of material that has a resistivity of $10^{-6} \Omega-\mathrm{m}$. If the energy is dissipated at rate 1.54 W in the resistor, then the current density is

A metal has $9 \times 10^{28}$ conduction electrons per $m^3$ and its resistivity is $1 \times 10^{-8} \Omega \mathrm{~m}$. If the drift speed of an electron in the metal is $1.6 \times 10^6 \mathrm{~m} / \mathrm{s}$, then its mean free path is (mass of electron $=9 \times 10^{-31} \mathrm{~kg}$ and charge of electron $=1.6 \times 10^{-19} \mathrm{C}$ )

The resistivity of a metal is $1 \times 10^{-8} \Omega-\mathrm{m}$. If it contains $9 \times 10^{28}$ electrons per $\mathrm{m}^3$, then the relaxation time of electrons inside the metal is nearly

(electron mass $=9 \times 10^{-31} \mathrm{~kg}$ )

A cylindrical metallic wire is stretched to increase its length in such a way that the metallic wire changes its resistance by $6 \%$. The percentage increase in its length is

Find the current in the three resistors as shown in the following figure?

The resistivity of a material is found to be $10^8 \Omega-\mathrm{m}$, then the material would be

A metal wire of length $L$ and radius $r$ has a resistance $R$. If a wire of the same metal of length $2 L$ and radius $3 r$ is taken, then what will be its resistance?

Balancing point of a potentiometer shifts from a length of 60 cm to 40 cm by shunting the cell with a $4 \Omega$ resistance. What is the internal resistance of the cell?

Four $4 \Omega$ resistors are connected together along the edges of a square. A 12 V battery with internal resistance of $2 \Omega$ is connected across a pair of the diagonally opposite corners of the square. The power dissipated in the circuit is

Find the equivalent resistance between point $A$ and $B$ in the following circuit. (The resistance of each resistor is $R$ )

In a meter bridge the balancing length from the left end is found to be 25 cm . The value of the unknown resistance is (assume, standard resistance of $1 \Omega$ is in the right gap)

A cylindrical wire $P$ has resistance $10 \Omega$. A second wire $Q$ has length and diameter half that of $P$. If the material of both the wires is same, then resistance of wire $Q$ is

Find the current in the circuit.

A conductor of length 100 cm and area of cross-section $1 \mathrm{~mm}^2$ carries a current of 5 A . If the resistivity of the material of the conductor is $3.0 \times 10^{-8} \Omega-\mathrm{m}$, then the electric field across the conductor is

If the Wheatstone's bridge with four resistors $R_1, R_2$ and $R_3, R_4$ is balanced, then the correct expression is

A moving coil galvanometer of resistance $100 \Omega$ is used as an ammeter using a resistance $0.1 \Omega$. The maximum deflection current in the galvanometer is $100 \mu \mathrm{~A}$. Find the minimum current in the circuit, so that ammeter shows maximum deflection?