In the circuit shown in the figure,$R = \sqrt{\frac{L}{C}}$. Switch $S$ is closed at time $t = 0$. The current through $C$ and $L$ would be equal after a time $t$ equal to

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.....$ms$

$A$ resistance $R$ and a capacitance $C$ are connected in series to a battery of negligible internal resistance through a key. The key is closed at $t = 0$. If after $t \, s$ the voltage across the capacitance is seven times the voltage across $R$,the value of $t$ is:

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

The charge across the capacitor in two different $RC$ circuits $1$ and $2$ are plotted as shown in the figure. Identify the correct statement$(s)$ related to the $R_1, R_2, C_1$ and $C_2$ of the two $RC$ circuits.

$A$ $20 \mu F$ capacitor is connected to a $45 \text{ V}$ battery through a circuit whose resistance is $2000 \Omega$. What is the final charge on the capacitor?