SSA of RLC circuit

Q.

Match the following.

Column 1	Column 2
The phase difference between current and voltage in a purely resistive ac circuit	$\frac{𝜋}{2}$, the current leads the voltage
The phase difference between current and voltage in a pure inductive ac circuit	$0$
The phase difference between current and voltage in a pure capacitive ac circuit	$\frac{𝜋}{2}$, current lags voltage
The phase difference between current and voltage in an LCR series circuit	$ta{n}^{-1}\left(X_C–\frac{X_L}{R}\right)$

Q. In a series RLC circuit, L = 40 mH is given. If the instantaneous voltage and current are $100\cos (314t-5^{\circ })V$ and $10\cos (314t-{50}^{\circ })A$ respectively, the value of R and C will be

1. $R=10\Omega andC=580\mu F$
2. $R=7.07\Omega andC=580\mu F$
3. $R=7.07\Omega andC=5.49mF$
4. $R=14.14\Omega andC=5.49mF$

Q. Consider a circuit shown below,
At steady state, the current through resistor is given by $15cost$ and the voltage across the inductor is $2\sin t$ .
The RMS value of the current through the capacitor is

1. $\frac{15}{\sqrt{2}}A$
2. $12\sqrt{2}A$
3. $7\sqrt{2}A$
4. $8\sqrt{2}A$

Q. For the circuit shown below the steady- state current is

1. 0 A
2. $5\sqrt{2}cos\left(1000t\right)A$
3. $5\sqrt{2}cos(1000t-\frac{\pi }{4})A$
4. $5\sqrt{2}A$

Q.

A series R-L-C circuit is excited with a 50 V, 50 Hz sinusoidal source. The voltages across the resistance and the capacitance are shown in the figure. The voltage across the inductor $V_L$ is V.

1. 50

Q. For a parallel RLC circuit, which one of the following statement is NOT correct?

1. The bandwidth of the circuit decreases if R is increased
2. The bandwidth of the circuit remains same if L is increased
3. At resonance, input impedance is a real quantity
4. At resonance, the magnitude of input impedance attains its minimum value

Q. In the circuit shown below, the current I is equal to

1. $1.4\angle 0{}^{\circ }A$
2. $2.0\angle 0{}^{\circ }A$
3. $2.8\angle 0{}^{\circ }A$
4. $3.2\angle 0{}^{\circ }A$

Q. For the network shown below, the source frequency $\omega$ at which applied voltage V and current I are in phase is

1. 5 rad/sec
2. 2 rad/sec
3. 3 rad/sec
4. 4 rad/sec