Typical Capacitor Charging/Discharging circuits

Optional Resistor

Charging Circuit Discharging Circuit

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1

0 2 4t

Q

Typical Capacitor Charging/Discharging circuits

Discharging CircuitAt 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

Discharging A Capacitor

Capacitor Discharge:• Rate of decay of charge is proportional to the

charge• Exponential decay

• Q = Q0e-t/RC

– But Q = VC, so Q0=V0C and VC = V0Ce-t/RC

• V = V0e-t/RC

– But V = IR, so V0=I0R and IR = I0Re-t/RC

• I = I0e-t/RC

This equation is on your data sheet.

This equation is NOT on your data sheet.

This equation is NOT on your data sheet.

Time Constant = RCRC – Time ConstantUnits is the Second!(or the Ohms . Farad)

When t = RC then

Q = Q0e-RC/RC

= Q0e-1

= Q0/e

Charge has fallen to 1/eth of its original value

When t = 2RC, Q= Q0/e2

Charge has fallen to 1/eth of 1/eth its original value

Note: e = 2.72, 1/e = 0.368 – about 37% 1/e2 = 0.135

How do we use this information?

Now have a go at Q 2 &3 P101 from AQA A2It may help to look at the worked example on P 99

6.5V / e = 2.39V6.5V / e2 = 0.88V

RC=2.5s 2RC=5.0s