Power dissipated in an L-C-R series circuit connected to an AC source of emf $\epsilon$ is 

(a) $\frac{{\epsilon }^{2}R}{\left[{\displaystyle R^2+{\left(L\omega -\frac{1}{C\omega }\right)}^2}\right]}$

(b) $\frac{{\epsilon }^2{\sqrt{R^2+\left(L\omega -{\displaystyle \frac{1}{C\omega }}\right)}}^2}{R}$

(c) $\frac{{\epsilon }^2\left[R^2+{\left(L\omega -{\displaystyle \frac{1}{C\omega }}\right)}^2\right]}{R}$

(d) $\frac{{\epsilon }^{2}R}{\sqrt{R^2+{\left(L\omega -{\displaystyle \frac{1}{C\omega }}\right)}^2}}$

The natural frequency of the circuit shown in the figure is:
    

1. $\frac{1}{2\mathrm{\pi }\sqrt{\mathrm{LC}}}$

2. $\frac{1}{\mathrm{\pi }\sqrt{\mathrm{LC}}}$

3. $\frac{2}{\mathrm{\pi }\sqrt{\mathrm{LC}}}$

4. None of these

The root-mean-square value of an alternating current of 50 Hz frequency is 10 A. The time taken by  the alternating current in reaching from zero to maximum value and peak value will be:

(1) 2×10^–2 s and 14.14 A            (2)  1 × 10^–2 s and 7.07 A

(3) 5×10^–3 s and 7.07 A              (4) 5 × 10^–3 s and 14.14 A

Match List I (expression for current) with List II (rms value of current) and select the correct answer.

Turn ratio in a step-up transformer is 1: 2 if a
Lechlanche cell of 1.5 V is connected across the
input, then the voltage across the output will be:

1. 0.1 V     

2. 1.5 V 

3. 0.75 V 

4. zero

In an ideal parallel LC circuit, the capacitor is
charged by connecting it to a D.C. source which
is then disconnected. The current in the circuit:

1. becomes zero instantaneously 
2. grows monotonically
3. decays monotonically
4. oscillates instantaneously

A power transmission line feeds input power at 2300V to a step down transformer with its primary windings having 4000 turns, giving the output power at 230 V. If the current in the primary of the transformer is 5A, and its efficiency is 90%, the output current would be:

1. 50 A

2. 45 A

3. 25 A

4. 20 A

At a moment (t = 0), when the charge on capacitor C₁ is zero, the switch is closed. If I₀ be the current through inductor at t = 0 , for t > 0                               

1. maximum current through inductor equals I₀/2.    

2. maximum current through inductor equals $\frac{{\mathrm{C}}_1{\mathrm{I}}_0}{{\mathrm{C}}_1+{\mathrm{C}}_2}$

3. maximum charge on ${\mathrm{C}}_1=\frac{{\mathrm{C}}_1{\mathrm{I}}_0\sqrt{{\mathrm{LC}}_2}}{{\mathrm{C}}_1+{\mathrm{C}}_2}$

4. maximum charge on ${\mathrm{C}}_1={\mathrm{C}}_1{\mathrm{I}}_0\sqrt{\frac{\mathrm{L}}{{\mathrm{C}}_1+{\mathrm{C}}_2}}$

A wire of resistance R is connected in series with an inductor of reactance $\mathrm{\omega }$L. Then quality factor of RL circuit is

1.  $\frac{R}{\omega L}$

2.  $\frac{\omega L}{\mathrm{R}}$

3.  $\frac{R}{\sqrt{R^2 + {\omega }^2{L}^2}}$

4.  $\frac{\omega L}{\sqrt{R^2 + {\omega }^2{L}^2}}$