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?

(a) $R=20\Omega , L=1.5H,C=35 \mu F$

(b) $R=25\Omega , L=2.5H,C=45 \mu F$

(c) $R=15\Omega , L=3.5H,C=30 \mu F$

(d) $R=25\Omega , L=1.5H,C=45 \mu F$

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°

An inductor 20 mH, a capacitor 50μF, and a resistor 40Ω are connected in series across a source of emf V=10sin340t. The power loss in the AC circuit is:

1. 0.67 W

2. 0.78W

3. 0.89 W

4. 0.46 W

A resistance 'R' draws power 'P' when connected to an AC source. If an inductance is now placed in series with the resistance, such that the impedance of the circuit becomes 'Z' the power drawn will be:

$1. P{\left(\frac{R}{Z}\right)}^2$
$2. P\sqrt{\frac{R}{Z}}$
$3. P\left(\frac{R}{Z}\right)$
$4. P$ 

A series R-C circuit is connected to an alternating voltage source. Consider two situations:

1. When the capacitor is air-filled.

2. When the capacitor is mica filled.

Current through the resistor is I and voltage across the capacitor is V then

(1)V_a<V_b

(2)V_a>V_b

(3)i_a>i_b

(4)V_a=V_b