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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. $\frac{2}{\sqrt{5}}$ 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. $100~\text{V}, 2~\text{A}$