$A$ capacitor is connected to a $20\, V$ battery through a resistance of $10\, \Omega$. It is found that the potential difference across the capacitor rises to $2\, V$ in $1\, \mu s$. The capacitance of the capacitor is $....\, \mu F$. Given: $\ln(10/9) = 0.105$.

In the circuit shown,the cells are ideal and of equal emfs $E$. The capacitance of the capacitor is $C$ and the resistance of the resistor is $R$. $X$ is first joined to $Y$ and then to $Z$. After a long time,the total heat produced in the resistor will be:

$A$ capacitor of capacitance $C$ is being discharged through a resistor $R$. Let $t_1$ be the time taken for the energy stored in the capacitor to reduce to half of its initial value,and $t_2$ be the time taken for the charge to reduce to one-fourth of its initial value. Find the ratio $t_1/t_2$.

An $RC$ circuit as shown in the figure is driven by an $AC$ source generating a square wave. The output wave pattern monitored by $CRO$ would look close to

In a $CR$ circuit, the growth of charge on the capacitor is

In the given circuit,switch $S$ is closed at $t = 0$. The current $I$ in the figure at time $t$ is