The current $I$,potential difference $V_L$ across the inductor,and potential difference $V_C$ across the capacitor in the circuit as shown in the figure are best represented vectorially as:

An induction coil has an impedance of $10\,\Omega$. When an $AC$ signal of frequency $1000\,Hz$ is applied to the coil,the voltage leads the current by $45^o$. The inductance of the coil is

$A$ capacitor of capacitance $100 \mu F$ and a coil of resistance $20 \Omega$ and inductance $12.5 mH$ are connected in series with a $220 V, \frac{200}{\pi} Hz$ $AC$ source. The maximum value of instantaneous current in the circuit is (in $A$)

An $AC$ circuit having supply voltage $E = 10 \sin \omega t$ consists of a resistor of resistance $R = 3 \Omega$ and an inductor of reactance $X_L = 4 \Omega$ as shown in the figure. The voltage across the inductor at $t = \pi / \omega$ is: (in $\text{ V}$)

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 $\Omega$)

The following series $L-C-R$ circuit,when driven by an emf source of angular frequency $70 \text{ krad/s}$,behaves effectively as: