Derivation of C = Q/V
- Rearrange the capacitor equation to make charge, Q the subject:
- The capacitance, C of a capacitor is fixed
- It is determined during the manufacturing process
- Hence, Q is directly proportional to V
Investigation with a Test Circuit
- The relationship between potential difference across and charge stored on can be investigated experimentally by charging a capacitor using a constant current
- A suitable test circuit contains:
- A parallel plate capacitor
- Switch
- Battery
- Ammeter
- Variable Resistor
- Voltmeter connected in parallel with the capacitor
A Test Circuit to Charge a Capacitor Using a Constant Current
The potential difference across and charge stored on a capacitor is investigated using this test circuit
- Close the switch and constantly adjust the variable resistor to keep the charging current at a constant value for as long as possible
- This will be impossible when the capacitor is close to fully charged
- Record the potential difference across the capacitor at regular time intervals until it equals the potential difference of the power supply
- Plot a graph of charging current and time taken to charge
- Once the capacitor is fully charged the current passing through it drops to zero
A Graph of Charging Current and Time Taken to Charge created using test circuit
The current-time graph of the capacitor in the test circuit whilst constantly adjusting the variable resistor
- Recall the equation for charge, current and time:
- Use it to calculate the charge stored on a capacitor at a given time
- Now plot a graph of the charge stored, Q against the potential difference at each recorded time interval
A Graph of Calculated Charge Against Potential Difference
The charge-potential difference graph of a capacitor is a straight line through the origin
- The calculated charge-potential difference graph is a straight line through the origin
- Hence, Q and V are directly proportional
- The gradient of the graph is constant and equal to the given capacitance of the capacitor, C
- So,