The capacitance of $C_1$ and $C_2$ shown in the diagram is $C$. $C_1$ is initially uncharged and $C_2$ is given a charge $2C\varepsilon$ as shown. Which of the following graph represents charge on plate $B$ of capacitor $C_2$ as a function of time?

For the given input voltage waveform $V_{\text{in}}(t)$,the output voltage waveform $V_0(t)$ across the capacitor is correctly depicted by:

$A$ capacitor $C = 100 \, \mu F$ is connected to three resistors,each of resistance $1 \, k\Omega$,and a battery of $emf$ $9 \, V$. The switch $S$ has been closed for a long time to charge the capacitor. When switch $S$ is opened,the capacitor discharges with a time constant of ...... $ms$.

$A$ $4 \mu F$ capacitor and a resistance of $2.5 \, M\Omega$ are in series with a $12 \, V$ battery. Find the time after which the potential difference across the capacitor is $3$ times the potential difference across the resistor. (Given $\ln(2) = 0.693$)

$A$ resistor $R$ and a $2 \ \mu F$ capacitor in series are connected through a switch to a $200 \ V$ direct supply. Across the capacitor is a neon bulb that lights up at $120 \ V$. Calculate the value of $R$ to make the bulb light up $5 \ s$ after the switch has been closed. (Given: $\log_{10} 2.5 = 0.4$)

$A$ 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: $\ln(10/9) = 0.105$.