When an $AC$ generator of $120 \, V$ is connected in series with a capacitor and a resistor of $30 \, \Omega$,the circuit carries a current of $1.5 \, A$. The potential difference across the capacitor will be ..... $V$.

For the $AC$ circuit shown in the figure,$R = 100 \ k\Omega$ and $C = 100 \ pF$. The phase difference between $V_{\text{in}}$ and $(V_B - V_A)$ is $90^{\circ}$. The input signal frequency is $10^x \ rad/sec$,where $x$ is . . . . . . .

When a coil is connected across a $20 \ V$ $DC$ supply,it draws a current of $5 \ A$. When it is connected across a $20 \ V, 50 \ Hz$ $AC$ supply,it draws a current of $4 \ A$. The self-inductance of the coil is .............. $mH$. (Take $\pi=3$)

In a series $R-C$ circuit shown in the figure,the applied voltage is $10\, V$ and the voltage across the capacitor is found to be $8\, V$. Then,the voltage across $R$ and the phase difference between the current and the applied voltage will respectively be

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 ...... .

In a series $LCR$ circuit,the voltages across the inductance and the capacitance are not