Derivation of C = Q/V (CIE A Level Physics)

• 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,