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

Current in an ac circuit is given by $\mathrm{i}=3 \sin \mathrm{\omega t}+4 \cos \mathrm{\omega t}$ then -

1.  rms value of current is 5 A

2.  mean value of this current in one half period will be $6/\mathrm{\pi }$

3.  if voltage applied is $\mathrm{V}={\mathrm{V}}_{\mathrm{m}} \sin \mathrm{\omega t}$ then the circuit must be containing resistance and capacitance.

4.  if voltage applied is $\mathrm{V}={\mathrm{V}}_{\mathrm{m}} \sin \mathrm{\omega t}$, the circuit may contain resistance and inductance.

Which of the following curves correctly represents the variation of capacitive reactance $\left({\mathrm{X}}_{\mathrm{C}}\right)$ with frequency n -

1.  

2.  

3.  

4.  

In the LCR series circuit, the voltmeter and ammeter readings are -

1.  E=100 volts, I=2 amp

2.  E=100 volts, I=5 amp

3.  E=300 volts, I=2 amp

4.  E=300 volts, I=5 amp

An AC voltage is applied to a resistance R and an inductor L in series. If R and the inductive reactance are both equal to 3 $\Omega$, the phase difference between the applied voltage and the current in the circuit is:

1.  $\frac{\mathrm{\pi }}{4}$

2.  $\frac{\mathrm{\pi }}{2}$

3.  zero

4.  $\frac{\mathrm{\pi }}{6}$