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) $\sqrt{3}/2$

The instantaneous values of alternating

current and voltages in a circuit are given

as 

$\mathrm{i}=\frac{1}{\sqrt{2}}\sin \left(100\mathrm{\pi t}\right) \mathrm{ampere}$
$\mathrm{e}=\frac{1}{\sqrt{2}}\sin (100\mathrm{\pi t}+\mathrm{\pi }/3) \mathrm{volt}$

The average power in Watts consumed in the

circuit is

(a) $\frac{1}{4}$

(b) $\frac{\sqrt{3}}{4}$

(c) $\frac{1}{2}$ 

(d) $\frac{1}{8}$

In an AC circuit an alternating voltage $\mathrm{e}=200 \sqrt{2} \sin 100\mathrm{t}$ volt is connected to a capacitor $1 \mathrm{\mu F}.$ The $\mathrm{rms}$ value of the current in the circuit is

(a) 100 mA

(b) 200 mA

(c) 20 mA

(d) 10 mA

The current i  in a coil varies with time as shown in the figure. The variation of induced emf with time would be

                  (a)                                                                                         (b)

                   (c)                                                                                             (d)

An \(AC\) voltage is applied to a resistance \(R\) and an inductor \(L\) in series. If \(R\) and the inductive reactance are both equal to \(3~ \Omega, \) then the phase difference between the applied voltage and the current in the circuit will be:

The rms value of potential difference V shown in the figure is

(1) ${\mathrm{V}}_{\mathrm{o}}$                                                     

(2) $\frac{{\mathrm{V}}_{\mathrm{o}}}{\sqrt{2}}$

(3)$\frac{{\mathrm{V}}_{\mathrm{o}}}{2}$                                                     

(4) $\frac{{\mathrm{V}}_{\mathrm{o}}}{\sqrt{3}}$   

A coil has resistance $30 \mathrm{\Omega }$ and inductive reactance $20 \mathrm{\Omega }$ at 50 Hz frequency. If an AC source of 200 V, 100 Hz, is connected across the coil, the current in the coil will be:

 1. $4.0 \mathrm{A}$                                          

 2. $8.0 \mathrm{A}$

 3. $\frac{20}{\sqrt{13}}\mathrm{A}$                                         

 4. $2.0 \mathrm{A}$