$A$ charged capacitor is allowed to discharge through a resistor by closing the key at the instant $t = 0$. At the instant $t = (\ln 4) \, \mu s$,the reading of the ammeter falls to half the initial value. The resistance of the ammeter is equal to

The charge on a capacitor of capacitance $10\,\mu F$ connected as shown in the figure is.......$\mu C$

Find the current from the battery at $(i)$ $t \rightarrow 0$ (initial) and $(ii)$ $t \rightarrow \infty$ (after a long time) when the switch is closed at $t = 0$.

An electric bulb, a capacitor, a battery, and a switch are all connected in series in a circuit. How does the intensity of light vary when the switch is turned on?

Given,
${R_1} = 1\,\Omega, R_2 = 2\,\Omega$
${C_1} = 2\,\mu F, C_2 = 4\,\mu F$
The time constants (in $\mu s$) for the circuits $I, II, III$ are respectively:

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