In the circuit shown, the charge $q$ varies with time $t$ as $q = t^2 - 5$, where $q$ is in coulomb and $t$ is in second. At time $t = 3$ second, the voltage $V_{AB}$ in volt will be:

$A$ resistor $R$, an inductor $L$, and a capacitor $C$ are connected in series with an a.c. source. When $L$ is removed from the circuit, the phase difference between voltage and current in the circuit is $\pi/3$. If instead, $C$ is removed from the circuit, the phase difference is again $\pi/3$. The power factor of the circuit is

In the circuit shown in the figure,the $ac$ source gives a voltage $V = 20\cos(2000t)$. Neglecting source resistance,the voltmeter and ammeter readings will be:

$A$ direct current of $4\,A$ and an alternating current of peak value $4\,A$ flow through resistances of $3\,\Omega$ and $2\,\Omega$ respectively. The ratio of heat produced in the two resistances in the same interval of time will be.

$A$ $\frac{2.5}{\pi} \mu F$ capacitor and $3000 \, \Omega$ resistor are joined in series to an $AC$ source of $200 \, V$ and $50 \, Hz$ frequency. The power factor of the circuit and the power dissipated in it will respectively be:

In an $A.C.$ circuit,the current: