An inductor of $20~\text{mH}$, a capacitor of $100~\mu \text{F}$, and a resistor of $50~\Omega$ are connected in series across a source of emf, $V=10 \sin (314 t)$. What is the power loss in this circuit?
1. $0.79 ~\text{W}$
2. $0.43 ~\text{W}$
3. $2.74 ~\text{W}$
4. $1.13 ~\text{W}$

The potential differences across the resistance, capacitance and inductance are $80$ V, $40$ V and $100$ V respectively in an $LCR$ circuit. What is the power factor of this circuit?
1. $0.4$
2. $0.5$
3. $0.8$
4. $1.0$

A 100 $\Omega$ resistance and a capacitor of 100 $\Omega$ reactance are connected in series across a 220 V source. When the capacitor is 50% charged, the peak value of the displacement current is

1. 2.2 A             

2. 11A

3. 4.4A               

4. 11$\sqrt{2}$A

A small-signal voltage V(t)=V_o sinωt is applied across an ideal capacitor C 

1. over a full cycle, the capacitor C does not consume any energy from the voltage source

2. current I(t) is in phase with voltage V(t)

3. current I(t) leads voltage V(t) by 180°

4. current I(t) lags voltage V(t) by 90°

Which of the following combinations should be selected for better tuning of an $LCR$ circuit used for communication?
1. $R=20~\Omega ,~L=1.5~\text{H},~C=35~\mu \text{F}$
2. $R=25~\Omega ,~L=2.5~\text{H},~C=45~\mu \text{F}$
3. $R=15~\Omega ,~L=3.5~\text{H},~C=30~\mu \text{F}$
4. $R=25~\Omega ,~L=1.5~\text{H},~C=45~\mu \text{F}$