Maharashtra Board Solutions for Chapter: AC Circuits, Exercise 2: Exercises

An emf $e=e_0\sin \omega t$ applied to a series $\mathrm{L}-\mathrm{C}-\mathrm{R}$ circuit derives a current $\mathrm{I}={\mathrm{I}}_0\mathrm{sin\omega t}$ in the circuit. Deduce the expression for the average power dissipated in the circuit.

Answer in brief.

Show that in an AC circuit containing a pure inductor, the voltage is ahead of current by $\frac{\pi }{2}$ in phase.

If the effective current in a $50$ cycle AC circuit is $5 \mathrm{A}$, what is the peak value of current’? What is the current $\frac{1}{600} \sec$. after if was zero?

An AC circuit consists of only an inductor of inductance $2 \mathrm{H}$. If the current is represented by a sine wave of amplitude $0.25 \mathrm{A}$ and frequency $60 \mathrm{Hz}$, calculate the effective potential difference across the inductor $\left(\mathrm{\pi }=3.142\right)$

A capacitor of $100 \mathrm{\mu F}$, a coil of resistance $50 \Omega$ and an inductance $0.5 \mathrm{H}$ are connected in series with a $110 \mathrm{V}-50 \mathrm{Hz}$ source. Calculate the rms value of current in the circuit.

Find the capacity of a capacitor which when put in series with a $10 \Omega$ resistor makes the power factor equal to $0.5$. Assume an $80\mathrm{V}- 100\mathrm{Hz}$ AC supply.

Calculate the value of capacitance in picofarad, which will make $101.4$ micro henry inductance to oscillate with frequency of one megahertz.

A $100 \mathrm{\mu F}$ capacitor is charged with a $50 \mathrm{V}$ source supply. Then source supply is removed and the capacitor is connected across an inductance, as a result of which $5 \mathrm{A}$ current tiows through the inductance. Calculate the value of the inductance.