RC, LR and LC Circuits with D.C. and A.C. Sources

A $15.0$ $\text{μF}$  capacitor is connected to $220$ $\text{V,}$ $50$ $\text{Hz}$ source. The capacitive reactance and the RMS current would be:

A series LCR circuit is made by taking $R=100\mathrm{\Omega },L=\frac{2}{\pi }\mathrm{H},C=\frac{100}{\pi }\mathrm{\mu F}$ . This series combination is connected across an a.c. source of $220 \mathrm{V}, 50 \mathrm{Hz}$. Calculate (i) the impedance of the circuit and
(ii) the peak value of the current flowing in the circuit.
(iii) Calculate the power factor of this circuit.

An a.c. voltage,  $V=V_{\text{m}}\sin \omega t$ , is applied across a

(i) Series RC circuit in which the capacitative impedance is ‘a’ times the resistance in the circuit.

(ii) Series RL circuit in which the inductive impedance is ‘b’ times the resistance in the circuit.

Calculate the value of the power factor of the circuit in each case.

An a.c. source, of voltage $V=V_m \sin \omega t$, is applied across a series LCR circuit. Which of the following is the phasor diagram for the circuit when capacitative impedance exceeds the inductive impedance?

The instantaneous current and voltage of an AC circuit are given by $\mathrm{i}=10\sin \left(314\mathrm{t}\right) \mathrm{A}$ and $\mathrm{V}=100\sin \left(314\mathrm{t}\right) \mathrm{V}$. The power dissipation in the circuit is

A resistor of  $200\Omega$  and a capacitor of 15.0 $\text{μF}$  are connected in series to a 220 V, 50 Hz a.c. source. Calculate

​(i) The current in the circuit.

(ii) The rms voltage across the resistor and the capacitor.

The instantaneous current and voltage of an a.c. circuit are given by $I=10\sin 300t \mathrm{A}$ and $V=200\sin 300t \mathrm{V}$. What is the power dissipation in the circuit?

In a series LCR circuit, the voltage across an inductor, capacitor and resistor are $20 \mathrm{V}$, $20 \mathrm{V}$ and $40 \mathrm{V}$ respectively. What is the phase difference between the applied voltage and the current in the circuit?

Graph showing variation of current with frequency of $AC$ source in a series $LCR$ circuit is,

An $LR$ series circuit has $L=1 \mathrm{H}$ and $R=1 \mathrm{\Omega }$. It is connected across an emf of $2 \mathrm{V}$. The maximum rate which energy is stored in the magnetic field is:

In a circuit shown in the figure, the capacitor $C$ is initially uncharged and the key $K$ is open. In this condition, a current of $1 \mathrm{A}$ flows through the $1 \Omega$ resistor. The key is closed at time $t=t_0$. Which of the following statement(s) is(are) correct?

[Given : $e^{–1}=0.36$]

Consider an $\mathrm{LC}$ circuit, with inductance $L=0.1 \mathrm{H}$ and capacitance $C={10}^{-3} \mathrm{F}$, kept on a plane. The area of the circuit is $1 {\mathrm{m}}^2$. It is placed in a constant magnetic field of strength $B_0$ which is perpendicular to the plane of the circuit. At time $t=0$, the magnetic field strength starts increasing linearly as $B=B_0+\beta \mathrm{t}$ with $\beta =0.04 \mathrm{T} {\mathrm{s}}^{-1}$. The maximum magnitude of the current in the circuit is____$\mathrm{m} \mathrm{A}$.

In the given circuit each of the resistors is of $1\mathrm{k\Omega }$ resistance and each of the capacitors has $4\mu \mathrm{F}$ capacitance. What is the charge in the capacitor between the points $B$ and $F$?

A $100 \mathrm{\Omega }$  resistance is connected in series with a choke coil. When a $400 \mathrm{V}, 50 \mathrm{Hz}$  supply is applied to this combination, the voltage across the resistance and the choke coil are $200 \mathrm{V}$ and $300 \mathrm{V}$  respectively. Find the power consumed by the choke coil. Also, calculate the power factor of the choke coil and the power factor of the circuit.

In the LCR circuit shown in figure

In the $L-R$ circuit shown in the figure, the key $K$ is closed at time $t=0$.

Initially switch $S$ was closed for long time. Switch is opened at $t=0$. Take $V=12 \mathrm{V}$, $R=4 \mathrm{ohm}\text{,} C=1.0 \mathrm{\mu F}$. At time $t=RC\ln 2$