An $AC$ supply gives $30 \ V$ $rms$ which passes through a $10 \ \Omega$ resistance. The power dissipated in it is ...... $W$.

The same current is flowing in two alternating circuits. The first circuit contains only an inductor and the other contains only a capacitor. If the frequency of the alternating e.m.f. is increased,the values of current will

The frequency for which a $5 \mu F$ capacitor has a reactance of $\frac{1}{1000} \Omega$ is given by

Capacitive reactance of a capacitor in an $AC$ circuit is $3 \ k\Omega$. If this capacitor is connected to a new $AC$ source of double frequency,the capacitive reactance will become:

As shown in the figure,an inductor of inductance $L = 200 \, mH$ is connected to an $AC$ source of emf $220 \, V$ and frequency $f = 50 \, Hz$. The peak value of current is given by $\frac{\sqrt{a}}{\pi} \, A$. The value of $a$ is..........

$A$ series $LCR$ circuit is subjected to an $AC$ signal of $200 \,V, 50 \,Hz$. If the voltage across the inductor $(L=10 \,mH)$ is $31.4 \,V$,then the current in this circuit is $\qquad$