In a step-up transformer, the turn ratio is \(1:20\). The resistance of \(100~\Omega\) connected across the secondary is drawing a current of \(2~\text{A}\). What are the primary voltage and current respectively?
1. \(100~\text{V}, 0.5~\text{A}\)
2. \(200~\text{V},10~\text{A}\)
3. \(10~\text{V}, 40~\text{A}\)
4. \(10~\text{V}, 20~\text{A}\)

An ideal inductor of 20 H is joined in series with a resistance of 5 ohms and a battery of 5V. The current flowing in the circuit after 4s is ( in amperes)

$1.<mspace\; width="1em"></mspace>\frac{1}{e}$
$2.<mspace\; width="1em"></mspace>e$
$3.<mspace\; width="1em"></mspace>1-\frac{1}{e<mspace\; width="1em"></mspace>}$
$4.<mspace\; width="1em"></mspace>1-e$

The RMS value of the current in a series LCR circuit is plotted with angular frequency as shown below. The ohmic resistance is R, inductance is L and capacitance is C in the circuit. The value of the difference (${\omega }_2-{\omega }_1)<mspace\; width="1em"></mspace>$is

$1.<mspace\; width="1em"></mspace>\frac{R}{L}$
$2.<mspace\; width="1em"></mspace>\frac{L}{R}$
$3.<mspace\; width="1em"></mspace>\frac{1}{\sqrt{LC}}$
$4.<mspace\; width="1em"></mspace>\frac{1}{\sqrt{2LC}}$

In the circuit diagram shown below, the reading of the a.c. voltmeter is

1. 200 V

2. 100 V

3. $50\sqrt{2}<mspace\; width="1em"></mspace>V$

4. zero

In a series RLC alternating current circuit, the r.m.s. value of current is $l$, the average power loss in the circuit is

$1.<mspace\; width="1em"></mspace>l^2<mspace\; width="1em"></mspace>R$
$2.<mspace\; width="1em"></mspace>l^2<mspace\; width="1em"></mspace>\omega L$
$3.<mspace\; width="1em"></mspace>l^{2<mspace\; width="1em"></mspace>}\omega C<mspace\; width="1em"></mspace>$
$4.<mspace\; width="1em"></mspace>l^2<mspace\; width="1em"></mspace>\left(\omega L-\frac{1}{\omega C}\right)$

A step-down transformer transforms 200 V to 100 volts. If the current in primary and secondary coils are 6 A and 9.6 A respectively, the efficiency of the transformer is

1. 60%

2. 70%

3. 80%

4. 90%

An ideal inductor connected to a cell is shown in figure. Select the correct relations between readings of ammeters $A_1<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>A_2$ just after the switch is closed and a long time after closing the switch

$1.<mspace\; width="1em"></mspace>A_1>A_2<mspace\; width="1em"></mspace>;<mspace\; width="1em"></mspace>A_1<A_2$
$2.<mspace\; width="1em"></mspace>A_1>A_{2<mspace\; width="1em"></mspace>};<mspace\; width="1em"></mspace>A_2=A_1$
$3.<mspace\; width="1em"></mspace>A_1<A_2<mspace\; width="1em"></mspace>;<mspace\; width="1em"></mspace>A_1<mspace\; width="1em"></mspace><<mspace\; width="1em"></mspace>A_2$
$4.<mspace\; width="1em"></mspace>A_1<A_2<mspace\; width="1em"></mspace>;<mspace\; width="1em"></mspace>A_1<mspace\; width="1em"></mspace>=A_2$

The power dissipated in the following circuit will be about half of its maximum value at approximately

$1.<mspace\; width="1em"></mspace>\omega =<mspace\; width="1em"></mspace>1050<mspace\; width="1em"></mspace>rad/s$
$2.<mspace\; width="1em"></mspace>\omega =1000<mspace\; width="1em"></mspace>rad/s$
$3.<mspace\; width="1em"></mspace>\omega =950<mspace\; width="1em"></mspace>rad/s$
$4.<mspace\; width="1em"></mspace>Both<mspace\; width="1em"></mspace>\left(1\right)<mspace\; width="1em"></mspace>\&<mspace\; width="1em"></mspace>\left(3\right)$

An ac source of emf e=50 sin 100 $\pi t$ is connected across a circuit for which the phasor diagram is shown in the figure. The time difference between current and voltage applied across the circuit is

1. 1.25 ms

2. 1.33 ms

3. 1.67 ms

4. 1.85 ms

The instantaneous values of current (in ampere) and potential (in volt) in an A.C. circuit are I= 4 sin$\omega t$ and V=100cos$\left(\omega t-\begin{array}{c}\pi \\ 3\end{array}\right)$ respectively. The power factor of the circuit is

$1.<mspace\; width="1em"></mspace>\frac{1}{2<mspace\; width="1em"></mspace>}$
$2.<mspace\; width="1em"></mspace>\frac{1}{\sqrt{2}}$
$3.<mspace\; width="1em"></mspace>1$
$4.<mspace\; width="1em"></mspace>\frac{\sqrt{3}}{2}$