For the $RC$ circuit shown, the resistance is $R = 10.0\ W$, the capacitance is $C = 5.0\ F$ and the battery has voltage $\xi= 12$ volts . The capacitor is initially uncharged when the switch $S$ is closed at time $t = 0$. At some time later, the current in the circuit is $0.50\ A$. What is the magnitude of the charge across the capacitor at that moment?.......$µC$

A resistance of $40 \,\Omega$ is connected to a source of alternating current rated $220\, V , 50 Hz$. Find the time taken by the current to change from its maximum value to $ms$ value

Match the following

Currents                                     $r.m.s.$ values

(1)${x_0}\sin \omega \,t$                               (i)$ x_0$

(2)${x_0}\sin \omega \,t\cos \omega \,t$                  (ii)$\frac{{{x_0}}}{{\sqrt 2 }}$

(3)${x_0}\sin \omega \,t + {x_0}\cos \omega \,t$        (iii) $\frac{{{x_0}}}{{(2\sqrt 2 )}}$

The mean and $rms$ value of an alternating voltage for half cycle as shown in figure are  respectively:-

The voltage of an $ac$ source varies with time according to the equation $V = 100\sin \,\left( {100\pi t} \right)\cos \,\left( {100\pi t} \right)$ where $t$ is in seconds and $V$ is in volts. Then

In a circuit, the value of the alternating current is measured by hot wire ammeter as $10$ ampere. Its peak value will be......$A$