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

a$.$ Write the mathematical expressions for the voltages $v_C,$ and $v_{R_1}$ and the current $i_C$ after the switch is thrown into position $1.$

b$.$ Find the values of $v_C,v_{R_1},$ and $i_C$ when the switch is moved to position $2$ at $t=100ms.$

c$.$ Write the mathematical expressions for the voltages $v_C$ and $v_{R_2}$ and the current $i_C$ if the switch is moved to position $3$ at $t=200ms.$

d$.$ Plot the waveforms of $v_C,v_{R_2},$ and $i_C$ for the time period extending from $0$ to $300$ ms $.$

Problem $26.$