Let $f = 50\, Hz$ and $C = 100\, \mu F$ in an $AC$ circuit containing a capacitor only. If the peak value of the current in the circuit is $1.57\, A$,the expression for the instantaneous voltage across the capacitor will be (assuming current is $I = I_m \sin(\omega t)$):

Keeping the source frequency equal to the resonating frequency of the series $LCR$ circuit,if the three elements,$L, C$ and $R$ are arranged in parallel,show that the total current in the parallel $LCR$ circuit is minimum at this frequency. Obtain the $rms$ current value in each branch of the circuit given below.
Figure shows a series $LCR$ circuit connected to a variable frequency $230\; V$ source. $L=5.0\; H, C=80\; \mu F, R=40\; \Omega$.

Average power associated with an ideal inductor and ideal capacitor over a complete cycle of $a.c.$ is respectively

The rms value of conduction current in a parallel plate capacitor is $6.9\,\mu A$. The capacity of this capacitor,if it is connected to a $230\,V$ $AC$ supply with an angular frequency of $600\,rad/s$,will be $....\,pF$.

In a choke coil,the reactance $X_L$ and resistance $R$ are such that

$A$ pure inductor of $50.0 \ mH$ is connected to a source of $220 \ V$. The frequency of the source is $50 \ Hz$. The rms current in the circuit (in $A$) will be $......$.