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. $\sqrt{5}~\text{A}$ 

In an ac circuit the reactance of a coil is $\sqrt{3}$ times its resistance, the phase difference between the voltage across the coil to the current through the coil will be:
1. $\pi / 3$
2. $\pi / 2$
3. $\pi / 4$
4. $\pi / 6$

The power factor of an ac circuit having resistance (R) and inductance (L) connected in series and an angular velocity ω is 

1. $R/\omega L$

2. $R/{(R^2+{\omega }^2{L}^2)}^{1/2}$

3. $\omega L/R$

4. $R/{(R^2-{\omega }^2{L}^2)}^{1/2}$

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. $\dfrac{\sqrt{R^{2} + \omega^{2} L^{2}}}{V^{2}}$

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

In a circuit, $L, C$ and $R$ are connected in series with an alternating voltage source of frequency $f.$ The current leads the voltage by $45^{\circ}$. The value of $C$ will be:

In an LR-circuit, the inductive reactance is equal to the resistance R of the circuit. An e.m.f. $E=E_0\cos \left(\omega t\right)$ applied to the circuit. The power consumed in the circuit is:

1. $\frac{E_0^2}{R}$

2. $\frac{E_0^2}{2R}$

3. $\frac{E_0^2}{4R}$

4. $\frac{E_0^2}{8R}$

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

In the circuit given below, what will be the reading of the voltmeter 

1. 300 V

2. 900 V

3. 200 V

4. 400 V