Consider the RC circuit with

R $1=$ R $2=$ R $3=10\mathrm{.}0$ kW$,$

and C $=0\mathrm{.}20$ mF$.$

The initial condition is v C$(0+$

$)=3\mathrm{.}0$ V$.$

The source is

v S$($t$)=6\mathrm{.}0[1\mathrm{.}0-0\mathrm{.}5$ u$($t$)]=6\mathrm{.}0-3\mathrm{.}0$ u$($t$)$ V

$($a$)$ Use source transformation to obtain the lower

circuit for t $>0.$ Calculate V x and R x$.(6$ pts$.)$

$($b$)$ KCL at the upper right$-$hand corner gives the

DE: dv C$($t$)/$dt $+[1/($R xC$)]$ v C$($t$)=(1/$R xC$)$ V x

Determine the form of natural solution vCN$($t$)$ with a value for s$.(3$ pts$)$

$($c$)$ Determine the particular solution v CP$($t$).(3$ pts$)$

$($d$)$ Determine the complete solution v C$($t$)$ for t $>0.(3$ pts$.)$