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. \(R=25~\Omega ,~L=1.5~\text{H},~C=45~\mu \text{F}\)