A capacitor bank is designed to discharge $5.0 \mathrm{~J}$ of energy through a $10.0-\mathrm{k} \Omega$ resistor array in under $2.0 \mathrm{~ms}$. To what potential difference must the bank be charged, and what must the capacitance of the bank be?

During a physics demonstration, a fully charged $90.0-\mu \mathrm{F}$ capacitor is discharged through a $60.0-\Omega$ resistor. How long will it take for the capacitor to lose $80.0 \%$ of its initial energy?

In the movie Back to the Future, time travel is made possible by a flux capacitor, which generates $1.21 \mathrm{GW}$ of power. Assuming that a 1.00-F capacitor is charged to its maximum capacity with a $12.0-\mathrm{V}$ car battery and is discharged through a resistor, what resistance is necessary to produce a peak power output of $1.21 \mathrm{GW}$ in the resistor? How long would it take for a $12.0$-V car battery to charge the capacitor to $90.0 \%$ of its maximum capacity through this resistor?

The circuit shown in the figure has a switch, $\mathrm{S}$, two resistors, $R_1=1.00 \Omega$ and $R_2=$ $2.00 \Omega$, a $12.0-\mathrm{V}$ battery, and $\left.R_1\right\}$ a capacitor with $C=20.0 \mu \mathrm{F}$. After the switch is closed, what will the maximum charge on the capacitor be? How long after the switch has been closed will the capacitor have $50.0 \%$ of this maximum charge?

What is the time constant for the discharging of the capacitors in the circuit shown in the figure? If the $2.00-\mu \mathrm{F}$ capacitor initially has a potential difference of $10.0 \mathrm{~V}$ across its plates, how much charge is left on it after the switch has been closed for a time equal to half of the time constant?

Initially, switches $S_1$ and $\mathrm{S}_2$ in the circuit shown in the figure are open and the capacitor has a charge of 100 . $\mathrm{mC}$. About how long will it take after switch $\mathrm{S}_1$ is closed for the charge on the capacitor to drop to $5.00 \mathrm{mC}$ ?