Determine vct for t 0 if at t 0 the switch opens in the ci

Determine v_c(t) for t > 0 if at t = 0, the switch opens in the circuit below.

Solution

For t<0 capacitor is open circuited because the circuit is in seady state .now Voltage across capacitor using voltage division rule we get 12*6/9=8v.

For t>0 the system is in transient state . As the voltage across the capacitor doesn\'t change instantaneously the voltage across capacitor is 8 v.