If a current I given by $I_0\sin \left(\omega t-\frac{{\displaystyle \pi }}{{\displaystyle 2}}\right)$ flows in an ac circuit across which an ac potential of $E=E_0\sin \omega t$ has been applied, then the power consumption P in the circuit will be 

(1) $P=\frac{E_0{I}_0}{\sqrt{2}}$

(2) $P=\sqrt{2}{E}_0{I}_0$

(3) $P=\frac{E_0{I}_0}{2}$

(4) P = 0

In an ac circuit, the current is given by \(i=5\sin(100t-\frac{\pi}{2})\) and the ac potential is V = 200 sin(100t) volt. The power consumption is:

1. 20 W

2. 40 W

3. 1000 W

4. 0 

In an LCR circuit having L = 8.0 henry, C = 0.5 μF and R = 100 ohm in series, what is the resonance frequency?

1. 600 radian/sec

2. 600 Hz

3. 500 radian/sec

4. 500 Hz

A circuit consists of 3 ohms of resistance and 4 ohms of reactance. The power factor of the circuit is:

1. 0.4

2. 0.6

3. 0.8

4. 1.0

The power factor of a good choke coil is:

1. Nearly zero

2. Exactly zero

3. Nearly one

4. Exactly one

The phase difference between the current and voltage of LCR circuit in series combination at resonance is 

(1) 0

(2) π/2

(3) π

(4) –π

In a series LCR circuit, resistance \(R=10~\Omega\) and the impedance \(Z=20~\Omega\). The phase difference between the current and the voltage will be:

1. 30°

2. 45°

3. 60°

4. 90°

The power factor of an ac circuit having resistance (R) and inductance (L) connected in series and an angular velocity ω is 

(1) $R/\omega L$

(2) $R/{(R^2+{\omega }^2{L}^2)}^{1/2}$

(3) $\omega L/R$

(4) $R/{(R^2-{\omega }^2{L}^2)}^{1/2}$

In an LR-circuit, the inductive reactance is equal to the resistance R of the circuit. An e.m.f. $E=E_0\cos \left(\omega t\right)$ applied to the circuit. The power consumed in the circuit is:

(1) $\frac{E_0^2}{R}$

(2) $\frac{E_0^2}{2R}$

(3) $\frac{E_0^2}{4R}$

(4) $\frac{E_0^2}{8R}$

In the circuit shown in the figure, neglecting source resistance, the voltmeter and ammeter reading respectively will be:

1. 0 V, 3 A
2. 150 V, 3 A
3. 150 V, 6 A
4. 0 V, 8 A