$1.$ Draw a diagram of a circuit with a Resistor, a Capacitor, a Battery, and a Switch wired together in a closed loop $($in series$).$

$2.$ Assume the Battery is $12$ V$,$ the Resistor is $1200,$ and the Capacitor is $25$ nF:

a$.$ What is the time constant for the circuit?

b$.$ What is the maximum charge on the capacitor for the circuit?

c$.$ What is the rise time $($the time required to reach $90\%$ of the maximum charge on the capacitor$)$ for the circuit?

$3.$ Assume the switch is open and the capacitor is uncharged. At time $=0$ close the switch to complete the circuit.

a$.$ Plot the current in the circuit as a function of time up to $90\%$ maximum capacitor charge.

b$.$ Plot the voltage $($electric potential difference$)$ across the capacitor as a function of time to $90\%$ maximum capacitor charge.

c$.$ On the same graph, plot the voltage across the resistor as a function of time to $90\%$ maximum capacitor charge.

d$.$ Short the battery $($replace the batter with a wire$)$ and on the same graph, continue the plot of the voltage across the resistor and the voltage across the capacitor as a functions of time to $10\%$ maximum capacitor charge.