In a given series $LCR$ circuit,$R = 4\, \Omega, X_L = 5\, \Omega$ and $X_C = 8\, \Omega$. The current :-

Two resistors are connected in series across a $5\,V\,rms$ source of alternating potential. The potential difference across the $6\,\Omega$ resistor is $3\,V$. If $R$ is replaced by a pure inductor $L$ of such magnitude that the current remains the same,then the potential difference across $L$ is.......$V$.

An a.c. source of angular frequency $\omega$ is connected across a resistor $R$ and a capacitor $C$ in series. The current is observed as $I$. Now the frequency of the source is changed to $\omega/4$, (keeping the voltage unchanged) the current is found to be $I/3$. The ratio of resistance to reactance at frequency $\omega$ is

In the given circuit,the voltage across the inductor will be ..... $V$.

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

In the given circuit,the potential difference across the resistance is $54 \, V$ and the power consumed by it is $16 \, W$. If the $AC$ frequency is $60 \, Hz$,find the value of $L$ in $H$.