Discharge

In the circuit below the capacitor is charged and a steady current flows through the resistor.

As soon as the switch is opened the capacitor starts to discharge through the resistor. The decay of charge is exponential, i.e. the rate of flow of charge (the current) is proportional to the amount of charge left on the capacitor.

Just like if you put a hole in a bucket of water. the rate of flow of water out of the hole would be proportional to the amount of water left in the bucket. The value of the resistance will also affect how quickly the charge flows out of the capacitor. A large resistance would be like having a small hole in the bucket.

so dQ/dt is proportional to Q. Looks pretty exponential to me.

Example

A 470 µF capacitor is charged using a 12V power supply then discharged through a 5 kΩ resistor.

Calculate
a) the charge on the capacitor when fully charged
b) the charge 2s and 4s after discharging begins
c) the voltage across the capacitor at these times.

a)   Q = C V    =  470 x 10^-6 x 12      = 5.64 x 10^-3 C

b)   for t = 2s  Q = Q₀ e ^-t/RC    =   5.64 x 10-3  x  e ^{- ( 2 / 2.35)} =     ,  for t = 4s    =   5.64 x 10-3  x  e ^{- ( 4 / 2.35)} =   

c)   V = Q / C   =