D. C. Pandey Solutions for Chapter: Alternating Current, Exercise 13: [ Level 2 ]

An $AC$ voltage $V=V_0\sin 100 t$ is applied to the circuit, the phase difference between current and voltage is found to be $\frac{\mathrm{\pi }}{4},$ then

When an alternating voltage of $220 \mathrm{V}$ is applied across a device $P$, a current of $0.25 \mathrm{A}$ Flows through the circuit, and it leads the applied voltage by an angle $\frac{\mathrm{\pi }}{2} \mathrm{radian}$ . When the same voltage source is connected across another device $Q$, the same current is observed in the circuit but in phase with the applied voltage. What is the current when the same source is connected across a series combination of $P$ and $Q$.

An inductor $\left(X_{\mathrm{L}}=2 \mathrm{\Omega }\right)$ a capacitor $\left(X_{\mathrm{C}}=8 \mathrm{\Omega }\right)$ and a resistance $\left(R=8 \mathrm{\Omega }\right)$ are connected in series with an $AC$ source. The voltage output of $AC$ source is given by $V=10\cos \left(100\pi t\right)$

The instantaneous potential difference between points $A$ and $B$, when the applied voltage is $\frac{3^{th}}{5}$ of the maximum value of applied voltage is

A group of electric lamps having a total power rating of $1000 \mathrm{W}$ is supplied by an $AC$ voltage $E=200\sin \left(310t+60°\right)$ Then, the $rms$ value of the circuit current is 

One $10 \mathrm{V}, 60 \mathrm{W}$ bulb is to be connected to a $100 \mathrm{V}$ line. The required self-inductance of the inductor coil will be: $\left(f=50 \mathrm{Hz}\right)$

An alternating voltage $V=30\sin 50t+40\cos 50t$ is applied to a resistor of resistance $10 \mathrm{\Omega }$. The rms value of the current through resistor is

Assertion: In $L-C-R$ series $AC$ circuit  $X_{\mathrm{L}}=X_{\mathrm{C}}=R$ at a given frequency. When this frequency is doubled, the impedance of the circuit is $\frac{\sqrt{13}}{2}R$.

Reason: The given frequency is resonance frequency.

Assertion: At resonance power factor of series $L-C-R$ circuit is zero.

Reason: At resonance current function and voltage functions are in the same phase.