Edexcel A Level (IAL) Physics-4.23 Core Practical 11: Investigating Capacitor Charge & Discharge- Study Notes- New Syllabus

CORE PRACTICAL 11: Display and Analyse the Charging and Discharging of a Capacitor

This core practical uses an oscilloscope or data logger to observe and analyse how the potential difference across a capacitor changes as it charges and discharges through a resistor. The experiment allows the time constant \( RC \) of the circuit to be determined.

 Aim  

To display and analyse the charging and discharging curves of a capacitor and determine the time constant \( RC \).

Theory

For a capacitor charging through a resistor:

\( V = V_0\left(1 – e^{-t/RC}\right) \)

For a capacitor discharging through a resistor:

\( V = V_0 e^{-t/RC} \)

The time constant of the circuit is:

\( \tau = RC \)

After one time constant:

• Charging: voltage reaches about 63% of its final value.
• Discharging: voltage falls to about 37% of its initial value.

Apparatus

• Capacitor
• Resistor
• d.c. power supply
• Switch (or signal generator)
• Oscilloscope or data logger with voltage sensor
• Connecting leads

 Method

1. Connect the capacitor and resistor in series with a d.c. power supply.
2. Connect the oscilloscope or data logger across the capacitor.
3. Set the oscilloscope time base and voltage scale appropriately.
4. Close the switch to allow the capacitor to charge.
5. Record the voltage–time charging curve.
6. Open the switch or change the circuit to allow the capacitor to discharge through the resistor.
7. Record the voltage–time discharging curve.

Graphs Obtained

• Charging: voltage rises exponentially with time.
• Discharging: voltage falls exponentially with time.
• The curves are initially steep and then gradually flatten.

Determining the Time Constant

Charging curve method:

• Find the final steady voltage \( V_0 \).
• Calculate \( 0.63V_0 \).
• The time taken to reach this voltage is the time constant \( RC \).

Discharging curve method:

• Find the initial voltage \( V_0 \).
• Calculate \( 0.37V_0 \).
• The time taken to fall to this voltage is the time constant \( RC \).

 Example Calculation

If a capacitor discharges from \( 5.0\ \mathrm{V} \):

\( 0.37V_0 = 0.37 \times 5.0 = 1.85\ \mathrm{V} \)

The time taken to reach \( 1.85\ \mathrm{V} \) is the time constant.

Safety Considerations

• Ensure correct polarity for electrolytic capacitors.
• Do not exceed the capacitor’s rated voltage.
• Discharge capacitors safely before altering the circuit.

Sources of Error and Improvements

• Internal resistance: oscilloscope and leads affect results.
• Component tolerances: actual \( R \) and \( C \) values may differ from nominal.
• Time resolution: use appropriate sampling rate.
• Repeat measurements and average results to reduce uncertainty.

Conclusion

• Charging and discharging curves are exponential.
• The time constant \( RC \) determines how quickly the capacitor responds.
• Oscilloscopes and data loggers allow accurate visualisation and analysis of capacitor behaviour.