For the network in Fig. $10\mathrm{.}92,$ composed of standard values:

a$.$ Find the mathematical expressions for the voltage $v_C$ and the current $i_C$ when the switch is thrown into position $1.$

b$.$ Find the mathematical expressions for the voltage $v_C$ and the current $i_C$ if the switch is thrown into position $2$ at a time equal to five time constants of the charging circuit.

c$.$ Plot the waveforms of $v_C$ and $i_C$ for a period of time extending from $0$ to $30s.$

FIG. $10\mathrm{.}92$

Problem $30.$

Please answer and dont skip any steps

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