For the series LCR circuit connected with $220 \mathrm{~V}, 50 \mathrm{~Hz}$ a.c source as shown in the figure, the power factor is $\frac{\alpha}{10}$. The value of $\alpha$ is $\_\_\_\_$ .

A capacitor C is first charged fully with potential difference of $V_0$ and disconnected from the battery. The charged capacitor is connected across an inductor having inductance L. In $t$ s, 25% of the initial energy in the capacitor is transferred to the inductor. The value of $t$ is ________ s.

A LCR series circuit driven with $E_{r m s}=90 \mathrm{~V}$ at frequency $f_{\mathrm{d}}=30 \mathrm{~Hz}$ has resistance $R=80 \Omega$, an inductance with inductive reactance $X_L=20.0 \Omega$ and capacitance with capacitive reactance $X_C=80.0 \Omega$. The power factor of the circuit is $\_\_\_\_$ .

An a.c. source of angular frequency $\omega$ is connected across a resistor $R$ and a capacitor $C$ in series. The current is observed as $I$. Now the frequency of the source is changed to $\omega / 4$, (keeping the voltage unchanged) the current is found to be $I / 3$. The ratio of resistance to reactance at frequency $\omega$ is

The figure given below shows an LCR series circuit with two switches S₁ and S₂. When switch S₁ is closed keeping S₂ open, the phase difference (φ) between the current and source voltage is 30° and phase difference is 60° when S₂ is closed keeping S₁ open. The value of (3L₁ − L₂) is ______ H.

An ac current is represented as

$i=5 \sqrt{2}+10 \cos \left(650 \pi t+\frac{\pi}{6}\right) A m p$

The r.m.s value of the current is

An alternating current is represented by the equation, $i=100 \sqrt{2} \sin (100 \pi t)$ ampere. The RMS value of current and the frequency of the given alternating current are

An alternating current is given by $\mathrm{I}=\mathrm{I}_{\mathrm{A}} \sin \omega \mathrm{t}+\mathrm{I}_{\mathrm{B}} \cos \omega \mathrm{t}$. The r.m.s current will be

A series LCR circuit is connected to an alternating source of emf E. The current amplitude at resonant frequency is $I_0$. If the value of resistance R becomes twice of its initial value then amplitude of current at resonance will be

A bulb and a capacitor are connected in series across an ac supply. A dielectric is then placed between the plates of the capacitor. The glow of the bulb :

A coil of negligible resistance is connected in series with $90 \Omega$ resistor across $120 \mathrm{~V}, 60 \mathrm{~Hz}$ supply. A voltmeter reads $36 \mathrm{~V}$ across resistance. Inductance of the coil is :

A LCR circuit is at resonance for a capacitor C, inductance L and resistance R. Now the value of resistance is halved keeping all other parameters same. The current amplitude at resonance will be now:

Given below are two statements :

Statement I : In an LCR series circuit, current is maximum at resonance.

Statement II : Current in a purely resistive circuit can never be less than that in a series LCR circuit when connected to same voltage source.

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

A series LCR circuit is subjected to an ac signal of $200 \mathrm{~V}, 50 \mathrm{~Hz}$. If the voltage across the inductor $(\mathrm{L}=10 \mathrm{~mH})$ is $31.4 \mathrm{~V}$, then the current in this circuit is _______.

An alternating voltage of amplitude $40 \mathrm{~V}$ and frequency $4 \mathrm{~kHz}$ is applied directly across the capacitor of $12 \mu \mathrm{F}$. The maximum displacement current between the plates of the capacitor is nearly :

Match List I with List II

	LIST I		LIST II
A.	Purely capacitive circuit	I.
B.	Purely inductive circuit	II.
C.	LCR series at resonance	III.
D.	LCR series circuit	IV.

Choose the correct answer from the options given below:

In an ac circuit, the instantaneous current is zero, when the instantaneous voltage is maximum. In this case, the source may be connected to :

A. pure inductor.

B. pure capacitor.

C. pure resistor.

D. combination of an inductor and capacitor.

Choose the correct answer from the options given below :

An AC voltage $V=20 \sin 200 \pi t$ is applied to a series LCR circuit which drives a current $I=10 \sin \left(200 \pi t+\frac{\pi}{3}\right)$. The average power dissipated is:

An alternating voltage $V(t)=220 \sin 100 \pi t$ volt is applied to a purely resistive load of $50 \Omega$. The time taken for the current to rise from half of the peak value to the peak value is:

Primary coil of a transformer is connected to $220 \mathrm{~V}$ ac. Primary and secondary turns of the transforms are 100 and 10 respectively. Secondary coil of transformer is connected to two series resistances shown in figure. The output voltage $\left(V_0\right)$ is :

A series L.R circuit connected with an ac source $E=(25 \sin 1000 t) V$ has a power factor of $\frac{1}{\sqrt{2}}$. If the source of emf is changed to $\mathrm{E}=(20 \sin 2000 \mathrm{t}) \mathrm{V}$, the new power factor of the circuit will be :

In an a.c. circuit, voltage and current are given by:

$V=100 \sin (100 t) V$ and $I=100 \sin \left(100 t+\frac{\pi}{3}\right) \mathrm{mA}$ respectively.

The average power dissipated in one cycle is:

A capacitor of capacitance $100 \mu \mathrm{F}$ is charged to a potential of $12 \mathrm{~V}$ and connected to a $6.4 \mathrm{~mH}$ inductor to produce oscillations. The maximum current in the circuit would be :

Primary side of a transformer is connected to $230 \mathrm{~V}, 50 \mathrm{~Hz}$ supply. Turns ratio of primary to secondary winding is $10: 1$. Load resistance connected to secondary side is $46 \Omega$. The power consumed in it is :

Given below are two statements:

Statement I : An AC circuit undergoes electrical resonance if it contains either a capacitor or an inductor.

Statement II : An AC circuit containing a pure capacitor or a pure inductor consumes high power due to its non-zero power factor.

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

Given below are two statements:

Statement I : When the frequency of an a.c source in a series LCR circuit increases, the current in the circuit first increases, attains a maximum value and then decreases.

Statement II : In a series LCR circuit, the value of power factor at resonance is one.

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

As per the given graph, choose the correct representation for curve $\mathrm{A}$ and curve B.

Where $\mathrm{X}_{\mathrm{C}}=$ reactance of pure capacitive circuit connected with A.C. source

$\mathrm{X}_{\mathrm{L}}=$ reactance of pure inductive circuit connected with $\mathrm{A} . \mathrm{C}$. source

R = impedance of pure resistive circuit connected with A.C. source.

$\mathrm{Z}=$ Impedance of the LCR series circuit $\}$

Given below are two statements:

Statement I : Maximum power is dissipated in a circuit containing an inductor, a capacitor and a resistor connected in series with an AC source, when resonance occurs

Statement II : Maximum power is dissipated in a circuit containing pure resistor due to zero phase difference between current and voltage.

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

A capacitor of capacitance $150.0 ~\mu \mathrm{F}$ is connected to an alternating source of emf given by $\mathrm{E}=36 \sin (120 \pi \mathrm{t}) \mathrm{V}$. The maximum value of current in the circuit is approximately equal to :

Match List - I with List - II :

Choose the correct answer from the options given below :

If $\mathrm{R}, \mathrm{X}_{\mathrm{L}}$, and $\mathrm{X}_{\mathrm{C}}$ represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless :

In a series LR circuit with $\mathrm{X_L=R}$, power factor P₁. If a capacitor of capacitance C with $\mathrm{X_C=X_L}$ is added to the circuit the power factor becomes P₂. The ratio of P₁ to P₂ will be :

For the given figures, choose the correct options :

In an LC oscillator, if values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of oscillator becomes $x$ times its initial resonant frequency $\omega_0$. The value of $x$ is :

A circuit element $\mathrm{X}$ when connected to an a.c. supply of peak voltage $100 \mathrm{~V}$ gives a peak current of $5 \mathrm{~A}$ which is in phase with the voltage. A second element $\mathrm{Y}$ when connected to the same a.c. supply also gives the same value of peak current which lags behind the voltage by $\frac{\pi}{2}$. If $\mathrm{X}$ and $\mathrm{Y}$ are connected in series to the same supply, what will be the rms value of the current in ampere?

An alternating emf $\mathrm{E}=440 \sin 100 \pi \mathrm{t}$ is applied to a circuit containing an inductance of $\frac{\sqrt{2}}{\pi} \mathrm{H}$. If an a.c. ammeter is connected in the circuit, its reading will be :

A coil of inductance 1 H and resistance $100 \,\Omega$ is connected to a battery of 6 V. Determine approximately :

(a) The time elapsed before the current acquires half of its steady - state value.

(b) The energy stored in the magnetic field associated with the coil at an instant 15 ms after the circuit is switched on. (Given $\ln 2=0.693, \mathrm{e}^{-3 / 2}=0.25$)

A transformer operating at primary voltage $8 \,\mathrm{kV}$ and secondary voltage $160 \mathrm{~V}$ serves a load of $80 \mathrm{~kW}$. Assuming the transformer to be ideal with purely resistive load and working on unity power factor, the loads in the primary and secondary circuit would be

The equation of current in a purely inductive circuit is $5 \sin \left(49\, \pi t-30^{\circ}\right)$. If the inductance is $30 \,\mathrm{mH}$ then the equation for the voltage across the inductor, will be :

$\left\{\right.$ Let $\left.\pi=\frac{22}{7}\right\}$

A series LCR circuit has $\mathrm{L}=0.01\, \mathrm{H}, \mathrm{R}=10\, \Omega$ and $\mathrm{C}=1 \mu \mathrm{F}$ and it is connected to ac voltage of amplitude $\left(\mathrm{V}_{\mathrm{m}}\right) 50 \mathrm{~V}$. At frequency $60 \%$ lower than resonant frequency, the amplitude of current will be approximately :

A direct current of $4 \mathrm{~A}$ and an alternating current of peak value $4 \mathrm{~A}$ flow through resistance of $3\, \Omega$ and $2\,\Omega$ respectively. The ratio of heat produced in the two resistances in same interval of time will be :

In a series $L R$ circuit $X_{L}=R$ and power factor of the circuit is $P_{1}$. When capacitor with capacitance $C$ such that $X_{L}=X_{C}$ is put in series, the power factor becomes $P_{2}$. The ratio $\frac{P_{1}}{P_{2}}$ is:

When you walk through a metal detector carrying a metal object in your pocket, it raises an alarm. This phenomenon works on :

To increase the resonant frequency in series LCR circuit,

In series RLC resonator, if the self inductance and capacitance become double, the new resonant frequency (f₂) and new quality factor (Q₂) will be :

(f₁ = original resonant frequency, Q₁ = original quality factor)

For a series LCR circuit, I vs $\omega$ curve is shown :

(a) To the left of $\omega$_r, the circuit is mainly capacitive.

(b) To the left of $\omega$_r, the circuit is mainly inductive.

(c) At $\omega$_r, impedance of the circuit is equal to the resistance of the circuit.

(d) At $\omega$_r, impedance of the circuit is 0.

Choose the most appropriate answer from the options given below :

If L, C and R are the self inductance, capacitance and resistance respectively, which of the following does not have the dimension of time?

The current flowing through an ac circuit is given by

I = 5 sin(120$\pi$t)A

How long will the current take to reach the peak value starting from zero?

A sinusoidal voltage V(t) = 210 sin 3000 t volt is applied to a series LCR circuit in which L = 10 mH, C = 25 $\mu$F and R = 100 $\Omega$. The phase difference ($\Phi $) between the applied voltage and resultant current will be :

Match List-I with List-II.

Choose the correct answer from the options given below :

If wattless current flows in the AC circuit, then the circuit is :

Given below are two statements :

Statement I : The reactance of an ac circuit is zero. It is possible that the circuit contains a capacitor and an inductor.

Statement II : In ac circuit, the average power delivered by the source never becomes zero.

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

A resistance of 40 $\Omega$ is connected to a source of alternating current rated 220 V, 50 Hz. Find the time taken by the current to change from its maximum value to the rms value :

An $LCR$ circuit is equivalent to a damped pendulum. In an $LCR$ circuit the capacitor is charged to ${Q_0}$ and then connected to the $L$ and $R$ as shown below :

If a student plots graphs of the square of maximum charge $\left( {Q_{Max}^2} \right)$ on the capacitor with time$(t)$ for two different values ${L_1}$ and ${L_2}$ $\left( {{L_1} > {L_2}} \right)$ of $L$ then which of the following represents this graph correctly ?
$\left( {plots\,\,are\,\,schematic\,\,and\,\,niot\,\,drawn\,\,to\,\,scale} \right)$