$A$ capacitor is connected to a cell of $emf$ $E$ having some internal resistance $r$. The potential difference across the

In the $RC$ circuit shown,the switch is closed at $t = 0$. Graphs showing the variation of potential $(V_R)$ across the resistor and potential $(V_C)$ across the capacitor are given. The time constant of the circuit is approximately equal to.....$ms$

Let $C$ be the capacitance of a capacitor discharging through a resistor $R$. Suppose $t_{1}$ is the time taken for the energy stored in the capacitor to reduce to half its initial value and $t_{2}$ is the time taken for the charge to reduce to one-fourth its initial value. Then the ratio $t_{1} / t_{2}$ will be

In the following circuit,the switch $S$ is closed at $t = 0.$ The charge on the capacitor $C_1$ as a function of time will be given by $\left( {{C_{eq}} = \frac{{{C_1}{C_2}}}{{{C_1} + {C_2}}}} \right).$

During the charging of a capacitor,the variation of the potential $V$ of the capacitor with time $t$ is shown as:

For the $RC$ circuit shown,the resistance is $R = 10.0\ \Omega$,the capacitance is $C = 5.0\ F$ and the battery has voltage $\xi = 12\ V$. 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 (in $C$)?