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Capacitor Charge

Physics: AQA A Level, topic 7.4.5

Charging a Capacitor

When the capacitor is charging up, the formulae (and graphs) are different.

Voltage

Voltage

  • The formula for this graph is:
  • V=V0(1−e−tRC)V=V_0(1-e^{-\frac{t}{RC}})
  • Where V0V_0 is the final potential difference across the capacitor.
Charge

Charge

  • The formula for this graph is:
  • Q=Q0(1−e−tRC)Q=Q_0(1-e^{-\frac{t}{RC}})
  • Where Q0Q_0 is the final charge across the capacitor.

Charging and Discharging a Capacitor - Experiment

We can perform an experiment to test theoretical predications about capacitors.

Safety warning

Safety warning

  • Some capacitors, called electrolytic capacitors, respond badly (i.e. they can explode) if they are charged incorrectly.
  • It matters which way round the terminals of the capacitor are connected to the terminals of the power supply.
  • You must take care to construct charging circuits with the correct polarity.
  • In practice, small non-electrolytic capacitors are often given to students for this section to avoid this.
Set up

Set up

  • A circuit should be set up as in the diagram.
Method - charging

Method - charging

  • Start with a discharged capacitor and the switch in position 2.
  • Put the switch in position 1 and start the stopwatch simultaneously.
  • Record the voltmeter and ammeter readings frequently.
  • Stop the stopwatch once the p.d. has increased to about 95% of the EMF of the battery.
Method - discharging

Method - discharging

  • Zero the stopwatch.
  • Start the stopwatch again, simultaneously switching the switch to position 2.
  • Record the voltmeter and ammeter readings frequently.
  • Stop the stopwatch once the p.d. has decreased to about 5% of the EMF of the battery.
Finding the time constant

Finding the time constant

  • The time constant is the time taken for the original p.d. to discharge to (1/e) times the original value.
  • This happens at 37% of the original value.
  • The time constant can be found by reading the time from a V-t graph directly, or multiplying the gradient of a ln(V)-t graph by (-1).
Finding the capacitance

Finding the capacitance

  • Once the time constant is calculated, the capacitance is the time constant divided by the resistance of the resistor.
  • Capacitance (C) = time constant (RC) ÷ resistance (R).
Obtaining quality data

Obtaining quality data

  • The challenge is to read and record the p.d. reading quickly enough because the reading can change rapidly.
  • The solution is to use a p.d. probe/digital voltmeter, connected to a datalogger and a computer.
  • The datalogger can take values of p.d. and time simultaneously, and without any reaction time issues connected with switching the switch and starting the stopwatch at the same time.

Test yourself on Capacitor Charge

  • Why is it important to charge a capacitor with the correct polarity?

  • Charging a capacitor

  • The time constant can be found by reading off the value of a voltage-time graph at what percentage of the initial voltage?

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