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

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 \(\omega\).

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:
       
1. \(0\)
2. \(\dfrac{I_0}{2}\)
3. \(\dfrac{2I_0 }{ \pi}\)
4. \(I_0\)

When an AC source of emf \(e = E_0 \sin (100t)\) is connected across a circuit, the phase difference between the emf \(e\) and the current \(i\) in the circuit is observed to be \(\frac{\pi}{4}\) as shown in the diagram. If the circuit consists only of \(RC\) or \(LC\) in series, then what is the relationship between the two elements?

In the diagram, two sinusoidal voltages of the same frequency are shown. What is the frequency and the phase relationship between the voltages?