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; \(i=5\sin\left(100t-\frac{\pi}{2}\right)\) and the AC potential is \(V =200\sin(100 t)~\text V.\) The power consumption is:
1. \(20~\text W\)
2. \(40~\text W\)
3. \(1000~\text W\)
4. zero

In an \(LCR\) circuit having \(L = 8.0~\text{H}\), \(C= 0.5~\mu\text{F}\) and \(R = 100~\Omega\) 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:

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. \(30^{\circ}\)
2. \(45^{\circ}\)
3. \(60^{\circ}\)
4. \(90^{\circ}\)

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. \(0~\text{V}, 3~\text{A}\)
2. \(150~\text{V}, 3~\text{A}\)
3. \(150~\text{V}, 6~\text{A}\)
4. \(0~\text{V}, 8~\text{A}\)