Impedance in RLC Circuit

Q. In the meter bridge circuit shown in figure, find the length AB for null deflection in galvanometer.

R=15Q R=10Q 

Q.

An AC circuit has $R=100\Omega$, $C=2\mu F$ and $L=80mH$, connected in series. The quality factor of the circuit is

1. $20$

2. $2$

3. $0.5$

4. $400$

Q.

A series LCR circuit is designed to resonate at an angular frequency ${\omega }_{\circ }={10}^{5}rad/s$. The circuit draws $16W$power from $120V$ source at resonance. The value of resistance$‘R’$ in the circuit is _______ $\Omega$.

Q. In adjoining LCR circuit, reading of which voltmeter will be zero at resonance condition ?

1. $V_3$
2. $V_1$
3. $V_2$
4. $V_4$

Q. Two circuits are shown in the figure (a) & (b). At a frequency of ${\text{rad s}}^{-1}$, the average power dissipated in one cycle will be the same in both the circuits.

Q. (a) Determine the value of phase difference between the current and the voltage in the given series LCR circuit.



(b) Calculate the value of additional capacitor which may be joined suitably to the capacitor C that would make the power factor of the circuit unity.

Q. A series R-C combination is connected to an AC voltage of angular frequency $\omega =500rad/s$. If the impedance of the R-C circuit is R $\sqrt{1.25}$, the time constant of the circuit in milliseconds upto two digits after the decimal point is
.

Q. In a Zener regulated power supply, a Zener diode with $V_Z=6.0\text{V}$ is used for regulation. The load current is to be $4.0\text{mA}$ and the unregulated input is $10.0\text{V}$. What should be the value of series resistor $R_S?$

1. $15\Omega$
2. $25\Omega$
3. $50\Omega$
4. $150\Omega$

Q. A series circuit consists of a resistance, inductor and capacitance. The applied voltage and the current at any instant are given by $E=141.4\cos (5000t–{10}^{\circ })\text{V}$ and $I=5\cos (5000t–{370}^{\circ })\text{A}$. The inductance of inductor is $0.01\text{H}$. Calculate the value of capacitance.

1. $1\mu F$
2. $6\mu F$
3. $4\mu F$
4. $5\mu F$

Q. A capacitor and resistor are connected with an AC source as shown in figure. Reactance of capacitor is $X_c=3\Omega$ and resistance of resistor is $R=4\Omega$ . The phase difference between $I$ and $I_1$ is degrees.

Q. A resistor and an inductor are connected to an $\text{AC}$ supply of $120\text{V}$ and $50\text{Hz}$. The current in the circuit is $3\text{A}$. If the power consumed in the circuit is $108W$, then the resistance in the circuit is

1. $12\Omega$
2. $40\Omega$
3. $\sqrt{(52\times 28)}\Omega$
4. $360\Omega$

Q. What is the power factor for the circuit shown?

Q. Given below are two statements.

Assertion : A choke coil is preferred over a resistor to adjust current in an AC circuit.

Reason : Power factor for inductance is zero, so, power loss is also zero for a full cycle.

Based on the above statements, choose the correct alternative.

1. Both assertion and reason are true, and the reason is a correct explanation of the assertion.
2. Both assertion and reason are true, but the reason is not a correct explanation of the assertion.
3. Assertion is true, but the reason is false.
4. Assertion is false, but the reason is true.

Q.

Given current of 4 A flows through an inductor of 2 H. What is the energy stored in inductor?

1. 4

2. 32

3. 16

4. 8

Q.

What is the voltage drop across a $1\mathrm{kW}$ electric heater element whose resistance, when hot, is $40\mathrm{\Omega }$?

Q. In an $\text{LCR}$ series circuit ܴ$R=1\Omega$, and $X_C=1000\Omega$ and ܺ$X_C=1000\Omega$. A source of $100\text{mV}$ is connected in the circuit the current in the circuit is_______ (in milli Ampere)

Q. In the shown figure, $X_c=100\Omega$, $X_L=200\Omega$ and $R=100\Omega$. The effective current through the source is

1. $2A$
2. $4A$
3. $2\sqrt{2}A$
4. $\sqrt{0.4}A$

Q. In the given circuit, the AC source has $\omega$ = 50 rad/s considering the inductor and capacitor to be ideal, the correct choice(s) is/are

1. The voltage across $100\Omega$ resistor = 20
2. The voltage across $50\Omega$ resistor = 20
3. The current through the circuit is $I=\frac{\sqrt{5}}{\sqrt{2}}A$
4. The current through the circuit is I = 1.2 A

Q. An electric lamp designed for operation on 110 V C is connected to a 220 V AC supply, through a choke coil of inductance 2H, for proper operation. The angular frequency of the AC is $100\sqrt{10}rad/s$ . If a capacitor is to be used in the place of the choke coil, its capacitance must be

1. $2\mu F$
2. $1\mu F$
3. $5\mu F$
4. $10\mu F$

Q. In a series circuit R = 300 $\Omega$ , L = 0.9 H, C = 2.0 $\mu$F and $\omega$ = 1000 rad/sec. The impendence of the circuit is

1. $400\Omega$
2. $1300\Omega$
3. $900\Omega$
4. $500\Omega$

Q.

When is a transistor said to be in active state? Draw a circuit diagram of a p-n-p transistor and explain how it works as a transistor amplifier. Write clearly, why in the case of a transistor (i) the base is thin and lightly doped and (ii) the emitter is heavily doped.

Q. In the given circuit, peak voltage across the resistor and capacitor are 6V and 8V. At an instant when voltage across capacitor is 4V in magnitude,

1. Voltage across resistance is $-3\sqrt{3}V$
2. Voltage across resistance is $3\sqrt{3}V$
3. Peak source voltage is $5\sqrt{3}$
4. Current in circuit is ahead of source voltage

Q. A circuit $\text{A}$ takes a current of $3\text{A}$ at a power factor of $0.6$ lagging when connected to a $115\text{V},50\text{Hz}$ supply. Another circuit $\text{B}$ takes a current of $5\text{A}$ at a power factor of $0.707$ leading when connected to the same supply. If the two circuits are connected in series across a $230\text{V},50\text{Hz}$ supply. Calculate the power consumed in the circuit.

1. $125\text{W}$
2. $555.5\text{W}$
3. $1187.5\text{W}$
4. $1525.2\text{W}$

Q. (i) When an AC source is connected to an ideal inductor, show that the average power supplied by the source over a complete cycle is zero.

(ii) A lamp is connected in series with an inductor and an AC source. What happens to the brightness of the lamp when the key is plugged in and an iron rod is inserted inside the inductor ? Explain.

Q. An arc lamp requires a direct current of $10A$ and $80V$ to function. if it is connected to a $220V\left(rms\right)$, $50HzAC$ supply, the series inductor needed for It to work is close to :

1. $0.08H$
2. $0.044H$
3. $0.065H$
4. $80H$

Q. Five cells have been connected in parallel to form a battery. The emf and intenal resistances of the cells have been shown in figure. If a load resistance $R$ is connected to the battery, then

1. Current passing through the cell is maximum which has smallest value of internal resistance.
2. Current passing through the cell is maximum which has largest value of internal resistance.
3. Internal resistance of equivalent cell is larger than the internal resistance of any cell connected.
4. Equivalent emf is $\frac{80E}{31}$

Q.

An RLC circuit with $R=100\omega$ is connected across ac source of 200V and angular frequency 300 rad/s. When only capacitance is removed, the current lags behind voltage by ${60}^{\circ }$. When only inductance is removed, the current leads the voltage by ${60}^{\circ }$. The current in the circuit is: (in Ampere)___

Q. An ac-generator supplying voltage $E$ to a circuit which consists of a resistor of resistance $3\Omega$ and an inductor of reactance $4\Omega$ as shown in the figure. The voltage across the inductor at $t=\pi /\omega$ is

1. $2\text{volts}$
2. $10\text{volts}$
3. zero
4. $4.8\text{volts}$

Q. A series LCR circuit with $L=012H$, $C=480nF$, $R=23\Omega$ is connected to a $230V$ variable frequency supply.

Q. For series $L-C-R$, graph between peak current and frequency ($\omega$) shown in the figure below.
The correct order for $R_1,R_{2}and{R}_3$

1. $R_3>R_1>R_2$
2. $R_3>R_2>R_1$
3. $R_1>R_2>R_3$
4. $R_2>R_1>R_3$