In a circuit,$L, C$ and $R$ are connected in series with an alternating voltage source of frequency $f$. The current leads the voltage by $45^o$. The value of $C$ is

$A$ sinusoidal voltage $V_0 \sin \omega t$ is applied across a series combination of resistance $R$ and inductance $L$. The amplitude of the current in this circuit is

An $AC$ circuit has an inductor and a resistor of resistance $R$ in series,such that $X_L = 3R$. Now,a capacitor is added in series such that $X_C = 2R$. The ratio of the new power factor to the old power factor of the circuit is $\sqrt{5} : x$. The value of $x$ is ...... .

$A$ coil of inductance $0.1 H$ and resistance $110 \Omega$ is connected to a source of $110 V$ and $350 Hz$. The phase difference between the voltage maximum and the current maximum is

In a series $L-C-R$ circuit,the frequency of a $10 \, V$ $a.c.$ voltage source is adjusted in such a fashion that the reactance of the inductor measures $15 \, \Omega$ and that of the capacitor $11 \, \Omega$. If $R = 3 \, \Omega$,the potential difference across the series combination of $L$ and $C$ will be.....$V$.

$A$ charged capacitor discharges through a resistance $R$ with time constant $\tau$. The two are now placed in series across an $AC$ source of angular frequency $\omega = \frac{1}{\tau}$. The impedance of the circuit will be-