When an AC source of emf \(e = E_0 \sin (100t)\) is connected across a circuit, the phase difference between the emf \(e\) and the current \(i\) in the circuit is observed to be \(\frac{\pi}{4}\) as shown in the diagram. If the circuit consists only of \(RC\) or \(LC\) in series, then what is the relationship between the two elements?

   

1.	\(R=1~\text{k} \Omega, C=10 ~\mu \text{F}\)
2.	\(R=1~\text{k}\Omega, C=1~\mu \text{F}\)
3.	\(R=1 ~\text{k}\Omega, L=10 ~\text{H}\)
4.	\(R=1 ~\text{k}\Omega, L=1~\text{H}\)

In the diagram, two sinusoidal voltages of the same frequency are shown. What is the frequency and the phase relationship between the voltages?
        

        
1. \(a\)
2. \(b\)
3. \(c\)
4. \(d\)

Which of the following combinations should be selected for better tuning of an L-C-R circuit used for communication?

1. $R=20\Omega , L=1.5H,C=35 \mu F$

2. $R=25\Omega , L=2.5H,C=45 \mu F$

3. $R=15\Omega , L=3.5H,C=30 \mu F$

4. $R=25\Omega , L=1.5H,C=45 \mu F$

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°

A transformer having efficiency of 90% is working on 200 V and 3 kW power supply. If the current in the secondary coil is 6A, the voltage across the secondary coil and the current in the primary coil respectively are
1. 300V,15A
2. 450V,15A

3. 450V,13.5A

4. 600V,15A

In an electrical circuit R, L, C, and an AC voltage source are all connected in series. When L is removed from the circuit, the phase difference between the voltage and the current in the circuit is $\mathrm{\pi }/3.$ If instead, C is removed from the circuit, the phase difference is again $\mathrm{\pi }/3.$ The power factor of the circuit is

(1) 1/2                                           

(2) 1/$\sqrt{2}$

(3) 1                                             

(4) $\sqrt{3}/2$