B M Sharma Solutions for Chapter: Alternating Current, Exercise 3: DPP

The self-inductance of a choke coil is $10 \mathrm{mH}$. When it is connected with a $10 \mathrm{V}$ DC source, then the loss of power is $20 \mathrm{W}$. When it is connected with $10 \mathrm{V}$ AC source, loss of power is $10 \mathrm{W}$. The frequency of AC source will be

A group of electric lamps having a total power rating of $1000 \mathrm{W}$ is supplied by an ac voltage $E=200\sin \left(310t+60°\right)$. The r.m.s. value of the circuit current is

In an $LR$ circuit, the inductive reactance is equal to the resistance $R$ of the circuit. An emf $E=E_0\sin \left(\omega t\right)$ is applied to the circuit. The power consumed in the circuit is

An $LCR$ series circuit with a resistance of $100$ $\mathrm{\Omega }$ is connected to an ac source of $200 \mathrm{V}$ (r.m.s.) and angular frequency $300 \mathrm{rad} {\mathrm{s}}^{-1}$. When only the capacitor is removed, the current lags behind the voltage by $60°$. When only the inductor is removed, the current leads the voltage by $60°$. The average power dissipated is

In the circuit shown in figure, neglecting source resistance, the voltmeter and ammeter readings, respectively, will be

In the circuit shown in the figure, the ac source gives a voltage $V=20\cos \left(2000t\right)$. Neglecting source resistance, the voltmeter and ammeter readings will be

An ac source of angular frequency $\omega$ is fed across a resistor $R$ and a capacitor $C$ in series. The current registered is $I$. If now, the frequency of the source is changed to $\frac{\omega }{3}$ (but maintaining the same voltage), the current in the circuit is found to be halved. Calculate the ratio of reactance to resistance at the original frequency $\omega$.

The diagram shows a capacitor $C$ and a resistor $R$ connected in series to an ac source. $V_1$ and $V_2$ are voltmeters and $A$ is an ammeter.

Consider the following statements:

$\mathrm{I}$. Readings in $A$ and $V_2$ are always in phase.
$\mathrm{II}$. Reading in $V_1$ is ahead in phase with reading in $V_2$.
$\mathrm{III}$. Readings in $A$ and $V_1$ are always in phase.

Which of these statements are/is correct?