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

The charge on the capacitor of capacitance $C$ shown in the figure below will be

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:

$A$ light bulb,a capacitor,and a battery are connected in a series circuit as shown in the figure,with switch $S$ initially open. When the switch $S$ is closed,which one of the following is true?

The circuit shown in the figure consists of a charged capacitor of capacity $3\, \mu F$ and a charge of $30\, \mu C$. At time $t = 0,$ when the key is closed,the value of current flowing through the $5\, M\Omega$ resistor is $'x'\, \mu A$. The value of $'x'$ to the nearest integer is .........

In an $RC$ circuit while charging,the graph of $\log i$ versus time is as shown by the dotted line in the diagram,where $i$ is the current. When the value of the resistance is doubled,which of the solid curves best represents the variation of $\log i$ versus time?