When $L$, $C$, and $R$ are connected in series with an $AC$ source of frequency $f$, the current leads the voltage by a phase angle of $45^{\circ}$. What is the value of $C$?

An $LCR$ series circuit with a resistance of $100 \, \Omega$ is connected to an $ac$ source of $200 \, V \, (r.m.s.)$ and angular frequency $300 \, rad/s$. When only the capacitor is removed, the current lags behind the voltage by $60^o$. When only the inductor is removed, the current leads the voltage by $60^o$. The average power dissipated is.....$W$

Consider the parallel $LCR$ circuit shown in the figure. Find the net current $i$ and the phase of $i$. Show that $i = \frac{V}{Z}$. Find the impedance $Z$ for this circuit.

Obtain the relation for the voltage applied to a series $LCR$ circuit.

In a series $LR$ circuit,$X_L = 3R$. Now,a capacitor with $X_C = R$ is added in series. What is the ratio of the new power factor to the old power factor?

In the following circuit,the emf of the source is $E_0 = 200 \, V$,$R = 20 \, \Omega$,$L = 0.1 \, H$,and $C = 10.6 \, F$. If the frequency is variable,then the current at frequency $f = 0$ and $f = \infty$ is: