Exercise

At resonance what is the value of power factor in the case of $LCR$ series circuit? 

A bulb of resistance $10 \mathrm{ohm}$, connected to an inductor of inductance $L$, is in series with an ac source marked $100\mathrm{V}$, $50\mathrm{Hz}$. If the phase angle between the voltage and angle is $\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$4$}\right. \mathrm{radian}$, calculate the value of $L$.

The emf and current of an a.c circuit containing $L,C \mathrm{and} R$ are given by $\epsilon ={\epsilon }_0\sin wt and I=I_0\sin \left(wt+\varphi \right)$. Show that the average power of the circuit is $P_{avg}={\epsilon }_v{I}_v\cos \varphi$, where ${\epsilon }_v$ and $I_v$ stand for virtual emf and virtual current respectively.

A charged capacitor is connected across an inductor with a wire having practically no resistance. Show that the discharge of the capacitor is oscillatory. Find the frequency of oscillations.

A bulb and a capacitor are connected in series to a source of alternating current. What will happen on increasing the frequency of the current?

Sketch a graph to show how the reactance of

a capacitor varies as a function of frequency.

How much power is consumed in a purely capacitive, A.C. circuit?

How much reactance is provided by a capacitor in a steady DC circuit?