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-

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

Which of the following devices is not based on Faraday's law of electromagnetic induction?

1. AC generator

2. Speedometer

3. Induction motor

4. DC motor

Current l through an inductor is increasing according to $i=2t$. Variation of the rate of increment of its energy $\left(\frac{du}{dt}\right)$ with time t is correctly shown in the graph
  
1.                2. 
3.               4. 

A time-varying current is given by $l=5\sin \left(\omega t+\begin{array}{c}\pi \\ 6\end{array}\right)$ Its r.m.s. value is (symbols have usual meanings)

$1. 5\sqrt{5} A$
$2. 10 A$
$3. \frac{5}{\sqrt{2}} A$
$4. \frac{15}{\sqrt{2}}A$

An alternating voltage $V\sqrt{2}\sin \omega t$ at different frequencies is applied across a capacitor C as shown in the figure. Which of the following graphs between RMS current $(I)$$$ observed by an ammeter and angular frequency $\omega$ of voltage is correct?
          
1.              2. 
3.              4.