RLC Circuit

Q.

In the adjoining ac circuit, the voltmeter whose reading will be zero at resonance is

Q. Each capacitor in the figure has a capacitance of $10\mu \text{F}$. The emf of the battery is $100\text{V}$. Find the ratio of the energy stored in $b$ to $a$.

1. $4$
2. $0.25$
3. $25$
4. $0.4$

Q. For an AC circuit, calculate the average value of the current per cycle, for which time function of the current is shown in the figure.

1. $\frac{2I_0}{3}$
2. $\frac{I_0}{2}$
3. $\frac{I_0}{\sqrt{2}}$
4. $\frac{3I_0}{4}$

Q. Find the potential at node A.

1. $+\frac{4}{3}\text{V}$
2. $-\frac{2}{3}\text{V}$
3. $-\frac{5}{3}\text{V}$
4. $+\frac{5}{3}\text{V}$

Q. If A and B are identical bulbs which bulbs glows brighter$(omega=100rad/s)$

1. A
2. B
3. Both equally bright
4. Cannot say

Q. A series LCR circuit containing a resistor of $120\Omega$ has an angular resonant frequency $4\times {10}^{5}rad{s}^{-1}$. At resonance the voltages across resistor and inductor are 60 V and $40\text{V}$ respectively.
The value of capacitance C is

1. $\frac{1}{32}\mu F$
2. $\frac{1}{16}\mu F$
3. $32\mu F$
4. $16\mu F$

Q. Find the current flowing through the resistance $R_1$ of the circuit shown in figure, if the resistances are equal to $R_1=10\Omega$, $R_2=10\Omega$ and $R_3=10\Omega$, and the potential of points $1,2$ and $3$ are equal to $V_1=10\text{V}$, $V_2=6\text{V}$ and $V_3=5\text{V}$.

1. $0.3\text{A}$
2. $0.1\text{A}$
3. $0.4\text{A}$
4. $0.2\text{A}$

Q. In the circuit shown in the figure, the ac source gives a voltage $V=20cos\left(2000t\right)$. Neglecting source resistance, the ammeter reading will be

1. 0.47A
2. 0.47A
3. 2 A
4. 1.4 A

Q. In a given circuit, if RMS voltage across resistance and capacitor are 25 V and 30 V, then peak voltage across inductor will be

1. $5V$
2. $25V$
3. $5\sqrt{2}V$
4. $25\sqrt{2}V$

Q. A telephone wire of length 200 km has a capacitance of 0.014$\mu$F per km. If it carries an ac of frequency 2.5 kHz, what should be the value of an inductor required to be connected in series so that the impedance of the circuit is minimum

1. 0.35 mH
2. 35 mH
3. 1.4 mH
4. Zero

Q. A magnetic field exists in a smoke chamber shown perpendicular to the plane of paper (either upwards or downwards). A beam coming out of a radioactive material [consisting of $\alpha ,{\beta }^{-},\gamma$ particles, proton $\left(H^{+}\right)$, Neutron] enters into the chamber through a fine hole, the four rays are named as $A,B,C$ and $D$.
[Assume $\alpha ,{\beta }^{-},$ Neutron and proton have nearly the same velocity.]
$\begin{array}{cccc}& \text{Column-I}& & \text{Column-II}\\ \text{(A)}& A& \text{(P)}& \alpha \\ \text{(B)}& B& \text{(Q)}& {\beta }^{-}\\ \text{(C)}& C& \text{(R)}& \gamma \\ \text{(D)}& D& \text{(S)}& H^{+}\\ & & \text{(T)}& \text{Neutron}\end{array}$
Which of the following option has the correct combination considering column-I and column-II.

1. $A\to S;B\to P;C\to R,T;D\to Q$
2. $A\to T;B\to Q;C\to R,T;D\to Q$
3. $A\to S;B\to P;C\to P,Q,R,T;D\to Q$
4. $A\to P,S;B\to P,R;C\to R,T;D\to Q$

Q. In the circuit given below, what will be the reading of the voltmeter

1. 300 V
2. 900 V
3. 200 V
4. 400 V

Q. In the circuit shown below, what will be the readings of the voltmeter and ammeter

1. 800 V, 2A
2. 220 V, 1.1A
3. 220 V, 2.2 A
4. 100 V, 2A

Q. In the circuit given below, what will be the reading of the voltmeter

1. 300 V
2. 900 V
3. 200 V
4. 400 V

Q. In a given R-L-C circuit where $R=30\Omega$
$L=20mHandC=\frac{50}{3}\mu F$

1. reading of Ammeter is $\frac{2}{5}A$
2. reading of voltmeter $V_1$ is $6\sqrt{10}V$
3. reading of voltmeter $V_2$ is 8V
4. potential difference across AB can be greater than 20V at an instant.

Q. In the circuit shown in the figure, the ac source gives a voltage $V=20cos\left(2000t\right)$. Neglecting source resistance, the ammeter reading will be

1. 0.47A
2. 0.47A
3. 2 A
4. 1.4 A

Q. In a given L - C circuit, switch S is closed at t = 0, then

1. maximum charge on capacitor can be $2C\epsilon$.
2. when charge on capacitor is half of its maximum charge, current is maximum
3. Charge on capacitor is $\frac{\epsilon C}{2}$ at $t=\frac{\pi }{3}\sqrt{LC}$
4. Maximum charge on capacitor can be $\epsilon C$

Q. One 10 V, 60 W bulb is to be connected to 100 V line. The required induction coil has self inductance of value (f = 50 Hz)

1. 0.052 H
2. 2.42 H
3. 16.2 mH
4. 1.62 mH

Q. A series LCR circuit containing a resistor of $120\Omega$ has an angular resonant frequency $4\times {10}^{5}rad{s}^{-1}$. At resonance the voltages across resistor and inductor are 60 V and $40\text{V}$ respectively.
The value of capacitance C is

1. $\frac{1}{32}\mu F$
2. $\frac{1}{16}\mu F$
3. $32\mu F$
4. $16\mu F$

Q. A box P and a coil Q are connected in series with an ac source of variable frequency. The emf of the source is constant at $10\text{V}$. Box P contains a capacitance of $1\mu F$ in series with a resistance of $32\Omega$. Coil Q has a self inductance of 4.9 mH and a resistance of $68\Omega$ in series. The frequency is adjusted so that maximum current flows in P and Q.
The voltage across P is

1. $12\text{V}$
2. $7.7\text{V}$
3. $10\text{V}$
4. $24\text{V}$

Q. In an LCR circuit ohm. When capacitance C is removed, the current lags behind the voltage by $\frac{\pi }{3}$ . When inductance L is removed, the current leads the voltage by $\pi$. The impedance of the circuit is

1. 50 ohm
2. 100 ohm
3. 200 ohm
4. 400 ohm

Q. Two inductors of self inductance $L$ each and mutual inductance $M$ are connected in series as shown in the figure.
Here ${\epsilon }_0=100V$, $R=30\Omega ,L=2mH$
$\omega ={10}^{4}rad/s$.

1. Maximum current in the circuit may be 3.33 A.
2. Maximum current in circuit wil be 2A.
3. Maximum current in the circuit may be less than 2A.
4. Source voltage is ahead of current in circuit.

Q. A series LCR circuit containing a resistor of $120\Omega$ has an angular resonant frequency $4\times {10}^{5}rad{s}^{-1}$. At resonance the voltages across resistor and inductor are 60 V and $40\text{V}$ respectively.
The value of inductance L is

1. $0.1\text{mH}$
2. $0.2\text{mH}$
3. $0.35\text{mH}$
4. $0.4\text{mH}$

Q. A resistor R, an inductor L and a capacitor C are connected in series to an oscillator of frequency n. If the resonant frequency is , then the current lags behind voltage, when

1. n = 0
2. $n<n_r$
3. $n=n_r$
4. $n>n_r$

Q. If A and B are identical bulbs which bulbs glows brighter$(omega=100rad/s)$

1. A
2. B
3. Both equally bright
4. Cannot say

Q. In the circuit given below, what will be the reading of the voltmeter

1. 300 V
2. 900 V
3. 200 V
4. 400 V

Q. Find the potential at node A.

1. $+\frac{5}{3}\text{V}$
2. $-\frac{5}{3}\text{V}$
3. $-\frac{2}{3}\text{V}$
4. $+\frac{4}{3}\text{V}$

Q. A LCR circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring-mass damped oscillator having damping constant 'b', the correct equivalence will be

1. $L\leftrightarrow \frac{1}{b}$, $C\leftrightarrow \frac{1}{m}$, $R\leftrightarrow \frac{1}{k}$
2. $L\leftrightarrow k$, $C\leftrightarrow b$, $R\leftrightarrow m$
3. $L\leftrightarrow m$, $C\leftrightarrow k$, $R\leftrightarrow b$
4. $L\leftrightarrow m$, $C\leftrightarrow \frac{1}{k}$, $R\leftrightarrow b$

Q. The power factor of the circuit shown below is $1/\sqrt{2}.$ The capacitance of the circuit is equal to

1. $400\mu F$
2. $300\mu F$
3. $500\mu F$
4. $200\mu F$

Q. What will be the self inductance of a coil, to be connected in a series with a resistance of $\pi \sqrt{3}\Omega$ such that the phase difference between the emf and the current at 50 Hz frequency is ${30}^{\circ }$

1. 0.5 Henry
2. 0.03 Henry
3. 0.05 Henry
4. 0.01 Henry