$\mathrm{An} \mathrm{alternating} \mathrm{current} \mathrm{is} \mathrm{given} \mathrm{as} \mathrm{i} = {\mathrm{i}}_1 \cos \mathrm{\omega t} - {\mathrm{i}}_2 \sin \mathrm{\omega t}. \mathrm{The} \mathrm{rms} \mathrm{current} \mathrm{is} \mathrm{given} \mathrm{by}$

1.  $\frac{{\mathrm{i}}_1 + {\mathrm{i}}_2}{\sqrt{2}}$

2.  $\frac{\left|{\mathrm{i}}_1 + {\mathrm{i}}_2\right|}{\sqrt{2}}$

3.  $\sqrt{\frac{{\mathrm{i}}_1^2 + {\mathrm{i}}_2^2}{2}}$

4.  $\sqrt{\frac{{\mathrm{i}}_1^2 + {\mathrm{i}}_2^2}{\sqrt{2}}}$

A generator produces a voltage that is given by V = 240 sin 120 t, where t is in seconds. The frequency and r.m.s. voltage are 

(1) 60 Hz and 240 V

(2) 19 Hz and 120 V

(3) 19 Hz and 170 V

(4) 754 Hz and 70 V

A resistance of \(20~ \mathrm{ohms}\) is connected to a source of an alternating potential, \(V=220sin(100 \pi t).\) The time taken by the current to change from its peak value to its r.m.s value will be: 

In the circuit shown in the figure, the ac source gives a voltage $V=20\cos \left(2000\text{\hspace{0.17em}}t\right).$ Neglecting source resistance, the voltmeter and ammeter reading will be: 

(1) 0V, 0.47A

(2) 1.68V, 0.47A

(3) 0V, 1.4 A

(4) 5.6V, 1.4 A

The variation of the instantaneous current (I) and the instantaneous emf (E) in a circuit are shown in the figure. Which of the following statements is correct?

The output current versus time curve of a rectifier is shown in the figure. The average value of the output current in this case will be:

The current 'i' in an inductance coil varies with time 't' according to the following graph.

Which one of the following plots shows the variations of voltage in the coil?

(1)

(2)

(3)

(4)

The rms value of potential difference V shown in the figure is

(1) ${\mathrm{V}}_{\mathrm{o}}$                                                     

(2) $\frac{{\mathrm{V}}_{\mathrm{o}}}{\sqrt{2}}$

(3)$\frac{{\mathrm{V}}_{\mathrm{o}}}{2}$                                                     

(4) $\frac{{\mathrm{V}}_{\mathrm{o}}}{\sqrt{3}}$   

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

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