$A$ 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 $A$)

When alternating current is passed through an $L-R$ series circuit,the power factor is $\frac{\sqrt{3}}{2}$ and $R=50 \ \Omega$. If the frequency of the source is $50 \ Hz$,then the value of $L$ is (Assume $\pi \approx 3.14$):
$\left[\cos \frac{\pi}{6}=\frac{\sqrt{3}}{2}, \quad \sin \frac{\pi}{6}=\frac{1}{2}, \quad \tan \frac{\pi}{6}=\frac{1}{\sqrt{3}}\right]$

Which one of the following curves represents the variation of impedance $(Z)$ with frequency $(f)$ in a series $L-C-R$ circuit,when connected to an $AC$ source?

An $AC$ voltage $V = 5 \cos(1000t) \text{ V}$ is applied to an $L-R$ circuit of inductance $3 \text{ mH}$ and resistance $4 \text{ } \Omega$. The value of maximum current in the circuit is . . . . . . $A$.

For the $AC$ circuit shown, the phase difference between emf and current is $\frac{\pi}{4} \text{ rad}$ as shown in the graph. If the impedance of the circuit is $1414 \Omega$, then the values of $P$ and $Q$ are:

$A$ resistance of $200 \ \Omega$ and an inductor of $\frac{1}{2 \pi} \ H$ are connected in series to an a.c. voltage of $40 \ V$ and $100 \ Hz$ frequency. The phase angle between the voltage and current is