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1.

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

2.

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

3.

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

4. A resistance of \(20~ \Omega\) is connected to a source of an alternating potential, \(V=220\sin(100 \pi t).\) The time taken by the current to change from its peak value to its rms value will be: 

1.	\( 0.2~\text{sec}\)	2.	\( 0.25~\text{sec}\)
3.	\(25 \times10^{-3}~\text{sec}\)	4.	\(2.5 \times10^{-3}~\text{sec}\)

5.

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°

6. 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. \(R + 2\pi f L\)
2. \(\sqrt{R^{2} + 4 \pi^{2} f^{2} L^{2}}\)
3. \(\sqrt{R^{2} + L^{2}}\)
4. \(\sqrt{R^{2} + 2 \pi f L}\)

7.

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.	\(\tan^{- 1} \dfrac{4}{3}\)	2.	\(\tan^{- 1} \dfrac{3}{4}\)
3.	\(\tan^{- 1} \dfrac{3}{2}\)	4.	\(\tan^{- 1} \dfrac{2}{5}\)

8.

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

9. In an ac circuit, a resistance of \(R\) ohm is connected in series with an inductance \(L\). If the phase angle between voltage and current is \(45^{\circ}\), the value of inductive reactance will be:

1.	\(\frac{R}{4}\)
2.	\(\frac{R}{2}\)
3.	\(R\)
4.	Cannot be found with the given data

10.

In a series LCR circuit, resistance R = 10Ω and the impedance Z = 20Ω. The phase difference between the current and the voltage is 
(1) 30°
(2) 45°
(3) 60°
(4) 90°

11.

In the circuit shown below, the AC source has voltage \(V = 20\cos(\omega t)\) volts with \(\omega =2000\) rad/sec. The amplitude of the current is closest to:
           
1. \(2\) A
2. \(3.3\) A
3. $\mathrm{}$\(\frac{2}{\sqrt{5}}\) A
4. \(\sqrt{5}~\text{A}\) $$

12.

An inductor of inductance \(L\) and resistor of resistance \(R\) are joined in series and connected by a source of frequency \(\omega\). The power dissipated in the circuit is:

1.	\(\dfrac{\left( R^{2} +\omega^{2} L^{2} \right)}{V}\)	2.	\(\dfrac{V^{2} R}{\left(R^{2} + \omega^{2} L^{2} \right)}\)
3.	\(\dfrac{V}{\left(R^{2} + \omega^{2} L^{2}\right)}\)	4.	\(\dfrac{\sqrt{R^{2} + \omega^{2} L^{2}}}{V^{2}}\)

13.

In an \(LCR\) circuit, the potential difference between the terminals of the inductance is \(60\) V, between the terminals of the capacitor is \(30\) V and that between the terminals of the resistance is \(40\) V. The supply voltage will be equal to:
1. \(50\) V
2. \(70\) V
3. \(130\) V
4. \(10\) V

14.

One 10 V, 60 W bulb is to be connected to 100 V line. The required induction coil has a self-inductance of value: (f = 50 Hz) 
(1) 0.052 H
(2) 2.42 H
(3) 16.2 mH
(4) 1.62 mH

15.

In the circuit shown below, what will be the readings of the voltmeter and ammeter?
        
1. \(800~\text{V}, 2~\text{A}\)
2. \(300~\text{V}, 2~\text{A}\)
3. \(220~\text{V}, 2.2~\text{A}\)
4. \(100~\text{V}, 2~\text{A}\)