AQA A Level Physics

Revision Notes

7.7.4 Required Practical: Charging & Discharging Capacitors

Required Practical: Charging & Discharging Capacitors

Equipment List

Capacitor Equipment list, downloadable AS & A Level Physics revision notes

  • Resolution of measuring equipment:
    • Voltmeter = 0.1 V
    • Stopwatch = 0.01 s

The overall aim of this experiment is to calculate the capacitance of a capacitor. This is just one example of how this required practical might be carried out

Variables

  • Independent variable = time, 
  • Dependent variable= potential difference, V
  • Control variables:
    • Resistance of the resistor
    • Current in the circuit

Method

Capacitor Practical Apparatus, downloadable AS & A Level Physics revision notes

  1. Set up the apparatus like the circuit above, making sure the switch is not connected to X or Y (no current should be flowing through)
  2. Set the battery pack to a potential difference of 10 V and use a 10 kΩ resistor. The capacitor should initially be fully discharged
  3. Charge the capacitor fully by placing the switch at point X. The voltmeter reading should read the same voltage as the battery (10 V)
  4. Move the switch to point Y
  5. Record the voltage reading every 10 s down to a value of 0 V. A total of 8-10 readings should be taken
  • An example table might look like this:

Capacitor Discharge Example Table, downloadable AS & A Level Physics revision notes

Analysing the Results

  • The potential difference (p.d) across the capacitance is defined by the equation:

Voltage Discharge Equation_2

  • Where:
    • V = p.d across the capacitor (V)
    • V0 = initial p.d across the capacitor (V)
    • t = time (s)
    • e = exponential function
    • R = resistance of the resistor (Ω)
    • C = capacitance of the capacitor (F)
  • Rearranging this equation for ln(V) by taking the natural log (ln) of both sides:

Capacitor Straight Line Equation Derivation

  • Comparing this to the equation of a straight line: y = mx + c
    • y = ln(V)
    • x = t
    • gradient = -1/RC
    • c = ln(V0)
  1. Plot a graph of ln(V) against t and draw a line of best fit
  2. Calculate the gradient (this should be negative)
  3. The capacitance of the capacitor is equal to:7.7.4 Capacitance from Graident Equation

Capacitor Practical Example Graph, downloadable AS & A Level Physics revision notes

Evaluating the Experiment

Systematic Errors:

  • If a digital voltmeter is used, wait until the reading is settled on a value if it is switching between two
  • If an analogue voltmeter is used, reduce parallax error by reading the p.d at eye level to the meter
  • Make sure the voltmeter starts at zero to avoid a zero error

Random Errors:

  • Use a resistor with a large resistance so the capacitor discharges slowly enough for the time to be taken accurately at p.d intervals
  • Using a datalogger will provide more accurate results for the p.d at a certain time. This will reduce the error in the speed of the reflex needed to stop the stopwatch at a certain p.d
  • The experiment could be repeated by measuring the time for the capacitor to charge instead

Safety Considerations

  • Keep water or any fluids away from the electrical equipment
  • Make sure no wires or connections are damaged and contain appropriate fuses to avoid a short circuit or a fire
  • Using a resistor with too low a resistance will not only mean the capacitor discharges too quickly but also that the wires will become very hot due to the high current
  • Capacitors can still retain charge after power is removed which could cause an electric shock. These should be fully discharged and removed after a few minutes

Worked Example

A student investigates the relationship between the potential difference and the time it takes to discharge a capacitor. They obtain the following results:

Capacitor Worked Example Experiment Table, downloadable AS & A Level Physics revision notes

Calculate the value of the capacitance of the capacitor discharged.

The capacitor is labelled with a capacitance of 4200 µF. Calculate the relative percentage error of the value obtained from the graph and this true value of the capacitance.

Step 1: Complete the table

    • Add an extra column ln(V) and calculate this for each p.d

Capacitor Worked Example Experiment Table (2), downloadable AS & A Level Physics revision notes

Step 2: Plot the graph of ln(V) against average time t

Capacitor Discharged Worked Example Graph (1), downloadable AS & A Level Physics revision notes

    • Make sure the axes are properly labelled and the line of best fit is drawn with a ruler

Step 3: Calculate the gradient of the graph

Capacitor Discharged Worked Example Graph (2), downloadable AS & A Level Physics revision notes

    • The gradient is calculated by:

Step 4: Calculate the capacitance, C

7.7.4 Capacitance from Graident Equation

Step 5: Calculate the relative percentage error of the value obtained

Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
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