1. AQA Physics Gravitational Fields, Electric Fields and Capacitance Section 9 Charging and Discharging a Capacitor

2. Charging a Capacitor A capacitor is usually charged in series with a resistor. The larger the resistance, the longer it takes the capacitor to charge. R

3. Charging a Capacitor The 10  F capacitor below is being charged with a 12V battery through a 24  resistor. 12V 0V 0A

4. Charging a Capacitor The 10  F capacitor below is being charged with a 12V battery through a 24  resistor. 12V 0V 12V 0.5A As soon as the switch is closed current starts to flow and the capacitor starts to charge. At t = 0s there is no potential difference across the capacitor.

5. Charging a Capacitor The 10  F capacitor below is being charged with a 12V battery through a 24  resistor. 12V 3V 9V 0.38A As the capacitor starts to charge a potential difference is created across it. This opposes the potential difference across the supply and reduces the potential difference across and current through the resistor. The rate at which the capacitor is being charged (the current) therefore starts to decrease.

6. Charging a Capacitor The 10  F capacitor below is being charged with a 12V battery through a 24  resistor. 12V 9V 3V 0.13A As the capacitor continues to charge the potential difference across it increases. This further opposes the potential difference across the supply and further reduces the potential difference across and current through the resistor. The rate at which the capacitor is being charged (the current) continues to decrease.

7. Charging a Capacitor The 10  F capacitor below is being charged with a 12V battery through a 24  resistor. 12V 0V 0A When the potential difference across the capacitor is equal to the potential difference of the supply an equilibrium is met. The two potential differences cancel each other out and there is no potential difference across, or current through the resistor.

8. Charging a Capacitor Q The gradient of the charge verses time graph is equal to the current through the charging circuit. The current is initially large because there is no potential difference across the capacitor to oppose the potential difference by the supply. The rate at which a capacitor is charged is not linear. The build up of charge is exponential. I V t t t Q0Q0 I0I0 V0V0

9. Discharging a Capacitor A capacitor is usually discharged in series with a resistor. The larger the resistance, the longer it takes the capacitor to discharge. R The circuit below shows a two way switch. In position 1 the capacitor is charged, in position 2 the capacitor is discharged. 1 2

10. Discharging a Capacitor The 10  F capacitor below is being discharged with a through a 24  resistor. 12V 0V 0A

11. Discharging a Capacitor The 10  F capacitor below is being discharged through a 24  resistor. 12V 0.5A Initially the potential difference across the capacitor (and hence the resistor) is at its maximum value. The rate at which the capacitor discharges (current) is therefore maximum at t = 0s.

12. Discharging a Capacitor The 10  F capacitor below is being charged with a 12V battery through a 24  resistor. 9V 0.38A As the capacitor discharges the potential difference across it (and hence the resistor) decreases. The rate at which the capacitor discharges (current) therefore starts to decrease.

13. Discharging a Capacitor The 10  F capacitor below is being charged with a 12V battery through a 24  resistor. 0V 0A When the capacitor discharges fully the potential difference across it (and hence the resistor) is zero. The rate at which the capacitor discharges (current) is therefore zero.

14. Discharging a Capacitor The rate at which a capacitor is discharges is not linear. The decrease in charge is exponential. The charge remaining of the capacitor (Q), the initial charge (Q 0 ), the resistance of the resistor (R), the capacitance of the capacitor (C) and the time (t) are related by the following equation: The term “RC” has the units of time and is therefore known as the time constant. The larger the time constant the longer it takes the capacitor to discharge.

15. Discharging a Capacitor Q The gradient of the charge verses time graph is equal to the current through the charging circuit. The current is initially large because the potential difference across the capacitor and hence the resistor is large. I t t Q0Q0 I0I0 The current (the rate of change at which the capacitor looses charge) decreases as the potential difference across the capacitor decreases. V t V0V0 The potential difference is proportional to the current and therefore follows the same pattern.

16. Discharging a Capacitor The following equations can be rearranged to make time the subject in the following way.