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:

In an $A.C.$ circuit,a resistance $R = 40 \ \Omega$ and an inductance $L$ are connected in series. If the phase angle between voltage and current is $45^{\circ}$,then the value of the inductive reactance is $(\tan 45^{\circ} = 1)$. (in $\Omega$)

In a simple $L-R$ circuit with an $A.C.$ source,the potential difference at any instant across the inductor and the resistor are $V_L$ and $V_R$ respectively,and the $A.C.$ source has a potential difference $V_{AC}$ at the same instant. Then:

An inductance of $0.2 \ H$ and resistance of $100 \ \Omega$ are connected in series to an $AC$ of $180 \ V$,$50 \ Hz$ supply. The $RMS$ current flowing in the circuit will be . . . . . . (Take $\pi^2$ as $10$). (in $A$)

When an $AC$ source of $e.m.f.$ $e = E_0 \sin(100t)$ is connected across a circuit,the phase difference between the $e.m.f.$ $e$ and the current $i$ in the circuit is observed to be $\pi/4$,as shown in the diagram. If the circuit consists possibly only of $RC$ or $LC$ in series,find the relationship between the two elements.

When an inductor $L$ and a resistor $R$ in series are connected across a $12 \, V, 50 \, Hz$ supply, a current of $0.5 \, A$ flows in the circuit. The current differs in phase from the applied voltage by $\frac{\pi}{3}$ radian. Then the value of $R$ is (in $\Omega$)