If i=2t, then the R.M.S. value of current between 0 to 2 second is

$1.<mspace\; width="1em"></mspace>\sqrt{\frac{2}{3}}$
$2.<mspace\; width="1em"></mspace>\frac{4}{\sqrt{3}}$
$3.<mspace\; width="1em"></mspace>\sqrt{\frac{5}{3}}$
$4.<mspace\; width="1em"></mspace>zero<mspace\; width="1em"></mspace>$

L, C, and R denote inductance, capacitance, and resistance respectively. pick out the combination which does not have the dimension of frequency.

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

The phase difference ($\varphi$) between emf and current in LCR series a.c. circuit is

$1.<mspace\; width="1em"></mspace>\varphi =<mspace\; width="1em"></mspace>0$
$2.<mspace\; width="1em"></mspace>0\le \varphi <\frac{\mathrm{\pi }}{2}$
$3.\frac{\mathrm{\pi }}{2}<\varphi <\mathrm{\pi }$
$4.<mspace\; width="1em"></mspace>\varphi =\mathrm{\pi }$

The primary and secondary coils of an ideal transformer have 100 and 5000 turns respectively. The magnetic flux linking the primary coil is given by $\varphi$= 20t + 10. The output voltage across the secondary coil is

1. 20 V

2. 500 V

3. 1000 V

4. 10000 V

In the LCR-circuit shown below, if the reading of the voltmeters $V_{1<mspace\; width="1em"></mspace>}$and $V_2$ are same, then

1. ${\omega }^2=\frac{1}{LC}$

2. Reading of the voltmeter V is 50 V

3. Reading of the ammeter A is 5 A

4. All of these

If \(R\) and \(L\) are resistance and inductance of a choke coil and \(f\) is the frequency of current through it, then the average power of the choke coil is proportional to:
1. \(R ~\)
2. \(\frac{1}{f^2}\)
3. \(\frac{1}{L^2}\)
4. All of these

Which of the following is/are copper loss/losses in a transformer?

1. Hysteresis loss

2. Eddy current loss

3. Heat loss in the primary and second coils

4. Both (1) & (2)

Half power frequencies for the circuit shown below are 200rad/s and 800 rad/s. The value of the product LC is $(is<mspace\; width="1em"></mspace>secon{d}^2/radia{n}^2)$

$1.<mspace\; width="1em"></mspace>6.25<mspace\; width="1em"></mspace>\times {10}^{-3}$
$2.<mspace\; width="1em"></mspace>6.25\times {10}^{-6}$
$3.<mspace\; width="1em"></mspace>1.25\times {10}^{-3}$
$4.<mspace\; width="1em"></mspace>1.25\times {10}^{-5}$

The power factor of the given circuit is: