$A$ $1 \mu F$ capacitor $C$ is connected to a battery of $10 V$ through a resistance of $1 \text{ M}\Omega$. The voltage across $C$ after $1 \text{ s}$ is approximately: (in $V$)

The circuit shown in the figure consists of a battery of $emf$ $\varepsilon = 10 \,V$,a capacitor of capacitance $C = 1.0 \, \mu F$,and three resistors of values $R_1 = 2 \, \Omega$,$R_2 = 2 \, \Omega$,and $R_3 = 1 \, \Omega$. Initially,the capacitor is completely uncharged and the switch $S$ is open. The switch $S$ is closed at $t = 0$.

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:

At $t = 0$,switch $S$ is closed. The charge on the capacitor is varying with time $t$ as $Q = Q_0(1 - e^{-\alpha t})$. Find the value of $Q_0$.

The switch $S$ shown in the figure is kept closed for a long time and then opened at $t = 0$. The current in the middle $20\, \Omega$ resistor at $t = 0.25\, ms$ is:

The capacitor shown in the figure is in a steady state. The energy stored in the capacitor is