S. L. Arora Solutions for Chapter: Alternating Current and Electrical Machines, Exercise 3: Problems For Practice

The virtual current in the a.c. circuit shown in Figure, is $1.0\mathrm{}\mathrm{A}$. Find (i) virtual voltage across the coil $\mathrm{L}$ (ii) impedance of the circuit and (iii) reactance of the coil.

A circuit containing a resistance of $50\mathrm{\Omega }$ and an inductance of $(1/\pi )$ H in series is connected to a $200\mathrm{}\mathrm{V}$ a.c. line of frequency $60\mathrm{}\mathrm{H}\mathrm{z}$. Find the reactance, the impedance, the current in the circuit and the phase difference between the alternating voltage and current.

An a.c. circuit consists of a $220\mathrm{}\mathrm{V},$ $50\mathrm{}\mathrm{H}\mathrm{z}$ supply connected across a $100\mathrm{\Omega }$ resistor. What inductance should be connected in the circuit in series with resistance so that the current is reduced to half?

A long solenoid connected to a $\mathrm{}12\mathrm{}\mathrm{V}$ d.c. source passes a steady current of $2\mathrm{}\mathrm{A}.$ When the solenoid is connected to an a.c. source of $12\mathrm{}\mathrm{V}$ at $50\mathrm{}\mathrm{H}\mathrm{z}$, the current flowing is $1\mathrm{}\mathrm{A}$. Calculate the inductance of the solenoid.

A choke coil and a resistance are connected in series in an a.c. circuit. A potential difference of $130 \mathrm{V}$ is applied to the circuit. If the potential difference across the resistance is $50 \mathrm{V}$, what should be the potential difference across the choke coil?

An emf, $\epsilon =200\sin 377t$ volt is applied across an inductance $L$ having a resistance of $1.0\mathrm{\Omega }$. The maximum current is found to be $10\mathrm{}\mathrm{A}$. Find the value of $L$.

An electric circuit containing an inductance $L$ and resistance $R$ in series has an impedance of $50\mathrm{\Omega }$ at $100\mathrm{H}\mathrm{z}$ and an impedance of $100\mathrm{\Omega }$ at $500\mathrm{}\mathrm{H}\mathrm{z}$. Find the values of $L$ and $R$.

In the RL-circuit shown in figure, resistance $R=30\mathrm{\Omega }$, reactance $X_L=40\mathrm{\Omega }$ and peak emf $=\mathrm{}220\mathrm{}\mathrm{V}$. 
Calculate the (i) impedance $Z.$ (ii) phase difference between the emf and current and (iii) the peak current $I_0$ in the circuit.