In the circuit shown, X is joining to Y for a long time, and then X is joined to Z. The total heat produced in $R_2$ is ( symbols have their usual meaning)

 $1. \frac{L{E}^2}{2{R_1}^2}$
$2. \frac{L{E}^2}{2{R_2}^2}$
$3.\frac{L{E}^2}{2R_1{R}_2}$
$4. \frac{L{E}^2{R}_2}{2{R_1}^3}$

A transformer has a turn ratio of 1: 5. A DC source of EMF 10 V is applied across its primary. EMF across the secondary will be

1. 50 V

2. 2 V

3. zero

4. 100 V

A series LCR circuit has resistance 2$\Omega$ and self inductance 20 mH. Bandwidth of the circuit is (in radian/s)

1. 1000

2. 100

3. 10

4. $\frac{1}{1000}$

Voltage across the resistor, inductor and capacitor in series LCR circuit are 20 V, 50 V and 50 V respectively. Peak value of the applied source is

1. 20 V

2. 20$\sqrt{2}$ V

3. 120$\sqrt{2}$ V

4. 120 V

The r.m.s value of current for

$l= 3\sin \omega t + 4 \cos \omega t is$

1. 5 A

2. 5$\sqrt{2}$ A

3. $\frac{5}{\sqrt{2}}A$

4. $\frac{7}{\sqrt{2}}A$

If ${\omega }_1$ and ${\omega }_2$ are half power frequencies of a series LCR circuit, then resonant frequency ${\omega }_r$ can be expressed as

$1. {\omega }_r=\frac{{\omega }_1+{\omega }_2}{2}$
$2. {\omega }_r=\sqrt{{\omega }_1{\omega }_2}$
$3. {\omega }_r=\sqrt{\frac{{{\omega }_1}^2+{{\omega }_2}^2}{2}}$
$4. {\omega }_r=\frac{{\omega }_1{\omega }_2}{{\omega }_1+{\omega }_2}$

The r.m.s. voltage of the waveform shown is:

1. 10 V

2. 6.37 V

3. 7 V

4. 10.5 v

Voltage and current in an A.C. circuit is given by $V=20\sin \left(314t\right) V and l=10\sin \left(314t+\frac{\pi }{3}\right) A.$

Wattful current in the circuit is-

$1. 10 A$
$2. 5 A$
$3. \frac{5}{\sqrt{2}}A$
$4. \frac{10}{\sqrt{2}}A$