S. L. Arora Solutions for Chapter: Alternating Current and Electrical Machines, Exercise 4: Problems For Practice

A circuit containing a $20\mathrm{\Omega }$ resistor and $0.1\mu \mathrm{F}$ capacitor in series is connected to $230\mathrm{}\mathrm{V}$ a.c. supply of angular frequency $100$rad $s^{-1}$. What is the impedance of the circuit?

A circuit consists of a resistance of $10\mathrm{\Omega }$ and a capacitance of $0.1\mu \mathrm{F}$. If an alternating emf of $100\mathrm{V}$, $50\mathrm{}\mathrm{H}\mathrm{z}$ is applied, find the current in the circuit.

A $20\mathrm{}\mathrm{W}$, $50\mathrm{}\mathrm{V}$, filament is connected in series to an a.c. mains of $250\mathrm{}\mathrm{V}$, $50\mathrm{}\mathrm{H}\mathrm{z}$. Calculate the value of the capacitor required to run the lamp.

Find the impedance of the circuit shown in figure, for (i) direct current and () alternating current of frequency $10/\pi \mathrm{k}\mathrm{H}\mathrm{z}$

A $1\mathrm{\mu }\mathrm{F}$ capacitor is connected to a $220\mathrm{}\mathrm{V}\mathrm{}-50\mathrm{}\mathrm{H}\mathrm{z}$ a.c. source. Find the virtual value of current through circuit. What is the peak value of voltage across the capacitor?

A capacitor in series with a resistance of $30\mathrm{\Omega }$ is connected to a.c. mains. The reactance of the capacitor is $40\mathrm{\Omega }$. Calculate the phase difference between the current and the supply voltage of capacitor.

A circuit has a resistance of $10\mathrm{\Omega }$ and its impedance is $100\sqrt{2}\mathrm{\Omega }$. Find the reactance of the circuit.