The potential difference V and the current i flowing through an instrument in an ac circuit of frequency f are given by $V=5\cos \omega t$ volts and I = 2 sin ωt amperes (where ω = 2πf). The power dissipated in the instrument is 

1. Zero

2. 10 W

3. 5 W

4. 2.5 W

A generator produces a voltage that is given by V = 240 sin 120 t, where t is in seconds. The frequency and r.m.s. voltage are 

1. 60 Hz and 240 V

2. 19 Hz and 120 V

3. 19 Hz and 170 V

4. 754 Hz and 70 V

The peak value of an alternating e.m.f. E is given by $E=E_0\cos \omega t$ is 10 volts and its frequency is 50 Hz. At time $t=\frac{1}{600}sec$, the instantaneous e.m.f. is

1. 10 V

2. $5\sqrt{3}V$

3. 5 V

4. 1 V

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:

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