For a series \(RLC\) circuit, \(R = X_L = 2X_C.\) The impedance of the circuit and phase difference between \(V\) and \(i\) will be: 

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:
       
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?
        

        
1. \(a\)
2. \(b\)
3. \(c\)
4. \(d\)

The potential differences across the resistance, capacitance and inductance are \(80\) V, \(40\) V and \(100\) V respectively in an \(LCR\) circuit. What is the power factor of this circuit?
1. \(0.4\)
2. \(0.5\)
3. \(0.8\)
4. \(1.0\)