The power factor of an $RL$ circuit is $1/2$. If $R = 100 \, \Omega$,what is the value of $L$? The frequency of the $AC$ source is $50 \, Hz$.

An alternating e.m.f. having voltage $V = V_0 \sin \omega t$ is applied to a series $L-C-R$ circuit. Given: $|X_L - X_C| = R$. The r.m.s. value of potential difference across the capacitor will be:

An alternating voltage is applied to a series $LCR$ circuit. If the current leads the voltage by $45^{\circ}$,then $\left(\tan 45^{\circ}=1\right)$:

An inductor of $\left(\frac{100}{\pi}\right) mH$,a capacitor of capacitance $\left(\frac{10^{-3}}{2 \pi}\right) F$,and a resistor of $10 \Omega$ are connected in series with an $AC$ voltage source of $110 \text{ V}, 50 \text{ Hz}$. The tangent of the phase angle $\phi$ between the voltage and the current is:

An inductor and a resistor are connected in series to an $AC$ source. The current in the circuit is $500 \,mA$, if the applied $AC$ voltage is $8 \sqrt{2} \,V$ at a frequency of $\frac{175}{\pi} \,Hz$, and the current in the circuit is $400 \,mA$, if the same $AC$ voltage at a frequency of $\frac{225}{\pi} \,Hz$ is applied. The values of the inductance and the resistance are respectively:

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.....$V$.