1. Typical Capacitor Charging/Discharging circuits Optional Resistor Charging CircuitDischarging Circuit

2. Typical Capacitor Charging/Discharging circuits Discharging Circuit At any time, when the PD across the capacitor = V then Q = C V = C I R = - C R dQ dt RC Rate of decay of charge is proportional to the charge on the capacitor

3. Discharging A Capacitor Capacitor Discharge: Rate of decay of charge is proportional to the charge Exponential decay Q = Q 0 e -t/RC –But Q = VC, so Q 0 =V 0 C and VC = V 0 Ce -t/RC V = V 0 e -t/RC –But V = I R, so V 0 = I 0 R and I R = I 0 Re -t/RC I = I 0 e -t/RC  This equation is on your data sheet.  This equation is NOT on your data sheet.

4. Time Constant = RC RC – Time Constant Units is the Second! (or the Ohms. Farad) When t = RC then Q = Q 0 e -RC/RC = Q 0 e -1 = Q 0 /e Charge has fallen to 1/e th of its original value When t = 2RC, Q= Q 0 /e 2 Charge has fallen to 1/e th of 1/e th its original value Note: e = 2.72, 1/e = 0.368 – about 37% 1/e 2 = 0.135

5. How do we use this information? Now have a go at Q 2 &3 P101 from AQA A2 It may help to look at the worked example on P 99 6.5V / e = 2.39V 6.5V / e 2 = 0.88V RC=2.5s 2RC=5.0s