7.4.5

# Capacitor Charge

Test yourself

## Charging a Capacitor

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

### Voltage

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

### Charge

• The formula for this graph is:
• $Q=Q_0(1-e^{-\frac{t}{RC}})$
• Where $Q_0$ 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

• 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

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

### 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

• 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

• 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

• 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

• 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.