In a circuit made up of resistance 4$\mathrm{\Omega }$ and inductance 0.01 H, an alternating emf 200 V at 50 Hz is connected, then the phase difference between the current and the emf in the circuit is :-

1.  ${\tan }^{-1}\left(\frac{\mathrm{\pi }}{4}\right)$

2.  ${\tan }^{-1}\left(\frac{\mathrm{\pi }}{3}\right)$

3.  ${\tan }^{-1}\left(\frac{\mathrm{\pi }}{2}\right)$

4.  ${\tan }^{-1}\left(\mathrm{\pi }\right)$

An electric bulb of (100 W, 300 V) is connected with an AC supply of 500 V and (150/$\mathrm{\pi }$)Hz. The required inductance to save the electric bulb is

1.  $2\mathrm{H}$

2.  $\frac{1}{2}\mathrm{H}$

3.  $4\mathrm{H}$

4.  $\frac{1}{4}\mathrm{H}$

A series LCR circuit is operated at resonance.

Assertion: The power transferred to the resistor is maximum

Reason: The current in the circuit is maximum

The peak value of an alternating e.m.f. E given by $E=E_0\cos \omega t$  is 10 volt and its frequency is 50 Hz. At a time t$=\frac{1}{600}$s the instantaneous value of the e.m.f. is-

1. 10 volt                                                     2. $5\sqrt{3}$ volt

3. 5 volt                                                       4. 1 volt

When an AC source of emf e = $E_0$ sin (100 t) is connected across a circuit, the phase difference between the emf e and the current i in the circuit is observed to be $\mathrm{\pi }/4$ as shown in the diagram. If the circuit consists possibly only of R-C or R-L or L-C series, find the relationship between the two elements.

1. $R = 1k \Omega , C = 10\mu F$                               2. $R = 1k \Omega , C = 1\mu F$

3. $R = 1k \Omega , L = 10H$                                4. $R = 1k \Omega , C = 1H$

The voltage time (V-t) graph for triangular wave having peak value $V_0$ is as shown in figure.

The rms value of V in time interval from t = 0 to T/4 is –

1. $\frac{V_0}{\sqrt{3}}$                                             2. $\frac{V_0}{2}$

3. $\frac{V_0}{\sqrt{2}}$                                             4. None of these

In $i_1=3\sin \omega t \mathrm{an}d i_2=4\cos \omega t i_3=i_1+i_2 then i_3$ is –

1. $5 \sin (\omega t + 53°)$                              2. $5 \sin (\omega t + 37°)$

3. $5 \sin (\omega t + 45°)$                            4. $5 \cos (\omega t + 53°)$

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.