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

A resistance of \(300~\Omega\) and an inductance of \(\frac{1}{\pi}\) henry are connected in series to an AC voltage of \(20\) volts and a \(200\) Hz frequency. The phase angle between the voltage and current will be:
1. \(\tan^{- 1} \frac{4}{3}\)

2. \(\tan^{- 1} \frac{3}{4}\)

3. \(\tan^{- 1} \frac{3}{2}\)

4. \(\tan^{- 1} \frac{2}{5}\)

In a region of uniform magnetic induction B = 10^–2 tesla, a circular coil of radius 30 cm and resistance π² ohm is rotated about an axis that is perpendicular to the direction of B and which forms a diameter of the coil. If the coil rotates at 200 rpm the amplitude of the alternating current induced in the coil is :

(1) 4π² mA

(2) 30 mA

(3) 6 mA

(4) 200 mA

In a LCR circuit having L = 8.0 henry, C = 0.5 μF and R = 100 ohm in series. The resonance frequency in radian per second is 

(1) 600 radian/second

(2) 600 Hz

(3) 500 radian/second

(4) 500 Hz

The impedance of a circuit consists of 3 ohm resistance and 4 ohm 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