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