$A$ resistance $R$ and a capacitance $C$ are connected in series to a battery of negligible internal resistance through a key. The key is closed at $t = 0$. If after $t \, s$ the voltage across the capacitance is seven times the voltage across $R$,the value of $t$ is:

$A$ circuit element is placed in a closed box. At time $t=0$,a constant current generator supplying a current of $1\, A$ is connected across the box. The potential difference across the box varies according to the graph shown in the figure. The element in the box is:

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

For the $RC$ circuit shown,the resistance is $R = 10.0\ \Omega$,the capacitance is $C = 5.0\ F$ and the battery has voltage $\xi = 12\ V$. The capacitor is initially uncharged when the switch $S$ is closed at time $t = 0$. At some time later,the current in the circuit is $0.50\ A$. What is the magnitude of the charge across the capacitor at that moment (in $C$)?

$A$ capacitor of capacitance $C = 10 \, \mu F$ is connected to a battery of emf $\varepsilon = 2 \, V$ through a resistor $R$. It is observed that it takes $t = 50 \, ms$ for the charge on the capacitor to reach $q = 12.6 \, \mu C$. Calculate the resistance $R$ of the circuit in $k \Omega$. (Take $1/e \approx 0.37$)

In the $R-C$ circuit shown in the figure, the total energy of $3.6 \times 10^{-3} \ J$ is dissipated in the $10 \ \Omega$ resistor when the switch $S$ is closed. The initial charge on the capacitor is ..... $\mu C$.