In the circuit above, V1 is a dc supply which outputs 12V, R1 has a value of 100 Ω and C1 is 100µF. The switch has been left in the position shown for a long time such that there is no stored energy in the capacitor. At time t=0, the switch is moved from position (b) to position (a).

a) For the instant that the switch is moved from (b) to (a), calculate the voltage across the capacitor and the current flowing through the resistor.

b) Calculate the voltage across the capacitor and current in the resistor when t = 0.025 seconds.

c) The switch is left in position (a) for enough time for capacitor C1 to be fully charged, t = t-charged. Sketch the graph of the voltage across the capacitor and the current flowing into it from t = 0 seconds until t = t-charged.

d) When the capacitor is fully charged, how much energy is it storing?

e) After t = t-charged, how much current is flowing through the resistor?

f) How much time after t=0 does it take for the voltage across the capacitor to reach 9V?

Ensure you show sufficient working out to support your answers.