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. \(\frac{\left( R^{2} +\omega^{2} L^{2} \right)}{V}\)
2. \(\frac{V^{2} R}{\left(R^{2} + \omega^{2} L^{2} \right)}\)
3. \(\frac{V}{\left(R^{2} + \omega^{2} L^{2}\right)}\)
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 \(45^{\circ}\). The value of \(C\) will be:
1. \(\frac{1}{2 \pi f \left( 2 \pi f L + R \right)}\)

2. \(\frac{1}{\pi f \left(2 \pi f L + R \right)}\)

3. \(\frac{1}{2 \pi f \left( 2 \pi f L - R \right)}\)

4. \(\frac{1}{\pi f \left(2 \pi f L - R \right)}\)

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 \(\omega\) 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 \(\frac{\omega}{3}\) (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 \(\omega\).
1. \(\sqrt{\frac{3}{5}}\)
2. \(\sqrt{\frac{2}{5}}\)
3. \(\sqrt{\frac{1}{5}}\)
4. \(\sqrt{\frac{4}{5}}\)

1. \(\frac{\sqrt{5} R}{2} ,\tan^{- 1} \left(2\right)\)

2. \(\frac{\sqrt{5} R}{2} , \tan^{- 1} \left(\frac{1}{2}\right)\)

3. \(\sqrt{5} X_{C} ,\tan^{- 1} \left(2\right)\)

4. \(\sqrt{5} R , \tan^{- 1} \left(\frac{1}{2}\right)\)

In a series \(LCR\) circuit, which one of the following curves represents the variation of impedance \((Z)\) with frequency \((f)\)?

1.		2.
3.		4.

The variation of the instantaneous current \((I)\) and the instantaneous emf \((E)\) in a circuit are shown in the figure. Which of the following statements is correct?

A constant voltage at different frequencies is applied across a capacitance C as shown in the figure.
          
Which of the following graphs accurately illustrates how current varies with frequency?

1.		2.
3.		4.

The output current versus time curve of a rectifier is shown in the figure. The average value of the output current in this case will be: