$[6\mathrm{.}25/12\mathrm{.}5$ Points$]$

SERCP$1118\mathrm{.}5.$OP$\mathrm{.}033.$

The figure below shows a capacitor, with capacitance $C=47\mathrm{.}5F,$ and a resistor, with resistance $R=70\mathrm{.}0k,$ connected in series to a battery, with $=29\mathrm{.}0V.$ The circuit has a switch, which is initially open.

$($a$)$ What is the circuit's time constant $($in s$)?$

s

$($b$)$ After the switch is closed for one time constant, how much charge $($in C $)$ is on the capacitor?

How does the charge on a capacitor, when charging, depend on the maximum charge, the time constant, and the elapsed time? How much time has elapsed? What is the maximum charge in terms of the capacitance and potential difference? C

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