Embibe Experts Solutions for Chapter: Alternating Current, Exercise 3: Exercise - 3

An $\mathrm{AC}$ voltage source of variable angular frequency $\omega$ and fixed amplitude $V_0$ is connected in series with a capacitor $C$ and an electric bulb of resistance $R$ (inductance zero). When $\mathrm{\omega }$ is in increased,

A series $R$-$C$ circuit is connected to an ac voltage source.  Consider two cases: (A) when $C$ is without a dielectric medium and

(B) when $\mathrm{C}$ is filled with a dielectric of constant $4$. The current  $I_{\mathrm{R}}$ through the resistor and voltage $V_{\mathrm{C}}$ across the capacitor are compared in the two cases. Which of the following is/are true?

The instantaneous voltages at three terminals marked $X,Y$ and $Z$ are given by $V_X=V_0\sin \omega t,V_Y=V_0\sin \left(\omega t+\frac{2\pi }{3}\right)$ and $V_Z=V_0\sin \left(\omega t+\frac{4\pi }{3}\right)$. An ideal voltmeter is configured to read rms value of the potential difference between its terminals. It is connected between points $X$ and $Y$ and then between $Y$ and $Z$. The reading(s) of the voltmeter will be

A circuit has a resistance of $12 \mathrm{\Omega }$ and an impedance of $15 \mathrm{\Omega }$ . The power factor of the circuit will be  

The phase-difference between the alternating current and emf is $\frac{\mathrm{\pi }}{2}$. which of the following cannot be the constituent of the circuit?

In a series $LCR$ circuit $R=200 \mathrm{\Omega }$ and the voltage and frequency of the main supply is $220 \mathrm{V}$ and $50 \mathrm{Hz}$ respectively. On taking out the capacitance from the circuit the current lags behind the voltage by $30°.$ On taking out the inductor from the circuit the current leads the voltage by $30°.$ The power dissipated in the $LCR$ circuit is

An arc lamp requires a direct current of $10 \mathrm{A}$ at $80 \mathrm{V}$ to function. If it is connected to a $220 \mathrm{V} \left(\mathrm{rms}\right)\text{, }50\mathrm{Hz} \mathrm{AC}$ supply, the series inductor needed for it to work is close to

An $LCR$ circuit is equivalent to a damped pendulum. In an $LCR$ circuit the capacitor is charged to $Q_0$ and then connected to the $L$ and $R$ as shown below:

If a student plots graphs of the square of maximum charge $\left({Q^2}_{\mathrm{Max}}\right)$ on the capacitor with time $\left(t\right)$ for two different values $L_1 \mathrm{and} L_2(L_1>L_2)$of $L$ then which of the following represents this graph correctly? (Plots are schematic and not drawn to scale)