$A$ 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 $100\, V$ $DC$ is applied across a solenoid,a current of $1\, A$ flows in it. When $100\, V$ $AC$ is applied across the same coil,the current drops to $0.5\, A$. If the frequency of the $AC$ source is $50\, Hz$,the impedance and inductance of the solenoid are:

For a series $LCR$ circuit, inductive reactance $X_L$ is equal to resistance $R$ and also equal to twice the capacitive reactance $X_C$. The impedance of the circuit and the phase difference between voltage $V$ and current $i$ are respectively

In a $L-R$ circuit of $4 \text{ mH}$ inductance and $3 \text{ } \Omega$ resistance, e.m.f. $E = \cos(1000t) \text{ V}$ is applied. The amplitude of current is (in $\text{ A}$)

$A$ series $L, R$ circuit connected with an ac source $E = (25 \sin 1000 t) \ V$ has a power factor of $\frac{1}{\sqrt{2}}$. If the source of emf is changed to $E = (20 \sin 2000 t) \ V$,the new power factor of the circuit will be:

In a series $LCR$ circuit, the $rms$ voltage across the resistor and the capacitor are $30 \ V$ and $90 \ V$ respectively. If the applied voltage is $V = 50 \sqrt{2} \sin \omega t$, then the peak voltage across the inductor is