A capacitor is charged to 
volts from a battery as shown in the diagram then
discharged through the resistor by throwing the switch to ground. Use the Laplace transform
method to calculate the current in the discharge. Look at the RC circuit example we
studied in lectures (there we applied a step function voltage to an uncharged capacitor).
In this case the applied voltage is zero for t>0 and we handle the initial condition (the charge on the capacitor) by writing the charge as:
Hence show that the initial charged condition is equivalent (for t>0) to applying
a step voltage 
to an uncharged capacitor at t=0.
Hence find the expression for the current I(t) for t>0.
SOLUTION :
For t>0 Kirchoff's voltage rule yields:
Taking the Laplace Transform:
Solving for 
gives:
Inverting the Laplace Transform then gives:
(Using 
)