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

A resistance of \(20~ \mathrm{ohms}\) is connected to a source of an alternating potential, \(V=220sin(100 \pi t).\) The time taken by the current to change from its peak value to its r.m.s value will be: 

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°

An alternating current of frequency ‘f’ is flowing in a circuit containing a resistance R and a choke L in series. The impedance of this circuit will be:

1. R + 2πfL

2. $\sqrt{R^2+4{\pi }^2{f}^2{L}^2}$

3. $\sqrt{R^2+L^2}$

4. $\sqrt{R^2+2\pi fL}$

A resistance of 300 Ω 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

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

L, C and R represent physical quantities inductance, capacitance and resistance respectively. The combination representing the dimension of frequency will be:

1. LC

2. (LC)^–1/2

3. ${\left(\frac{{\displaystyle L}}{{\displaystyle C}}\right)}^{-1/2}$

4. $\frac{C}{L}$