For the circuit in Fig. $10\mathrm{.}88,$ composed of standard values:

a$.$ Determine the time constant of the circuit.

b$.$ Write the mathematical equation for the voltage $v_C$ following the closing of the switch.

c$.$ Determine $v_C$ after one, three, and five time constants.

d$.$ Write the equations for the current $i_C$ and the voltage $v_R.$

e$.$ Sketch the waveforms for $v_C$ and $i_C.$

FIG. $10\mathrm{.}88$

Problem $23.$

Please do step by step

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