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. \(\sqrt{R^{2} + 2 \pi f L}\)

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. \(\tan^{- 1} \frac{4}{3}\)

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

3. \(\tan^{- 1} \frac{3}{2}\)

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

In the circuit shown below, the ac source has voltage $V=20\cos \left(\omega t\right)$ volts with ω = 2000 rad/sec.  The amplitude of the current is closest to:
         

1. 2 A

2. 3.3 A

3. $2/\sqrt{5}\mathrm{ \; A}$

4. $\sqrt{5}\mathrm{ \; A}$

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

1. $\frac{(R^2+{\omega }^2{L}^2)}{V}$

2. $\frac{V^{2}R}{(R^2+{\omega }^2{L}^2)}$

3. $\frac{V}{(R^2+{\omega }^2{L}^2)}$

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

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°. The value of C will be:

1. $\frac{1}{2\pi f(2\pi fL+R)}$

2. $\frac{1}{\pi f(2\pi fL+R)}$

3. $\frac{1}{2\pi f(2\pi fL-R)}$

4. $\frac{1}{\pi f(2\pi fL-R)}$

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. \(100~\text{V}, 2~\text{A}\)

An ac source of angular frequency ω is fed across a resistor r and a capacitor C in series. I is the current in the circuit. If the frequency of the source is changed to ω/3 (but maintaining the same voltage), the current in the circuit is found to be halved. Calculate the ratio of reactance to resistance at the original frequency ω.
1. $\sqrt{\frac{3}{5}}$
2. $\sqrt{\frac{2}{5}}$
3. $\sqrt{\frac{1}{5}}$
4. $\sqrt{\frac{4}{5}}$