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

An alternating current is given by the equation $i=i_1\cos \omega t+i_2\sin \omega t$. The r.m.s. current is given by

1. $\frac{1}{\sqrt{2}}(i_1+i_2)$

2. $\frac{1}{\sqrt{2}}{(i_i+i_2)}^2$

3. $\frac{1}{\sqrt{2}}{(i_1^2+i_2^2)}^{1/2}$

4. $\frac{1}{2}{(i_1^2+i_2^2)}^{1/2}$

Voltage and current in an ac circuit are given by $V=5\sin \left(100\pi t-\frac{{\displaystyle \pi }}{{\displaystyle 6}}\right)$ and $I=4\sin \left(100\pi t+\frac{{\displaystyle \pi }}{{\displaystyle 6}}\right)$ 

1. Voltage leads the current by 30°

2. Current leads the voltage by 30°

3. Current leads the voltage by 60°

4. Voltage leads the current by 60°

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:

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

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