CIE A Level Physics (9702) 2019-2021

Revision Notes

22.1.1 Capacitance

Defining Capacitance

  • Capacitors are electrical devices used to store energy in electronic circuits, commonly for a backup release of energy if the power fails
  • They can be in the form of:
    • An isolated spherical conductor
    • Parallel plates
  • Capacitors are marked with a value of their capacitance. This is defined as:

The charge stored per unit potential difference

  • The greater the capacitance, the greater the energy stored in the capacitor
  • A parallel plate capacitor is made up of two conductive metal plates connected to a voltage supply
    • The negative terminal of the voltage supply pushes electrons onto one plate, making it negatively charged
    • The electrons are repelled from the opposite plate, making it positively charged
    • There is commonly a dielectric  in between the plates, this is to ensure charge does not freely flow between the plates

Exam Tip

The ‘charge stored’ by a capacitor refers to the magnitude of the charge stored on each plate in a parallel plate capacitor or on the surface of a spherical conductor. The capacitor itself does not store charge.

Calculating Capacitance

  • The capacitance of a capacitor is defined by the equation:

Calculating Capacitance equation 1


  • Where:
    • C = capacitance (F)
    • Q = charge (C)
    • V = potential difference (V)
  • It is measured in the unit Farad (F)
    • In practice, 1 F is a very large unit
    • Capacitance will often be quoted in the order of micro Farads (μF), nanofarads (nF) or picofarads (pF)
  • If the capacitor is made of parallel plates, Q is the charge on the plates and V is the potential difference across the capacitor
  • The charge Q is not the charge of the capacitor itself, it is the charge stored on the plates or spherical conductor
  • This capacitance equation shows that an object’s capacitance is the ratio of the charge on an object to its potential

Capacitance of a Spherical Conductor

  • The capacitance of a charged sphere is defined by the charge per unit potential at the surface of the sphere
  • The potential V is defined by the potential of an isolated point charge (since the charge on the surface of a spherical conductor can be considered as a point charge at its centre):

Calculating Capacitance equation 2

  • Substituting this into the capacitance equation means the capacitance C of a sphere is given by the expression:

C = 4πε0r

Worked example: Charge on parallel plates

Calculating_Capacitance_Worked_example_-_Charge_on_Parallel_Plates_Question, downloadable AS & A Level Physics revision notes

Step 1:            Write down the known quantities

Capacitance, C = 1 nF = 1 × 10-9 F

Potential difference, V = 0.3 kV = 0.3 × 103 V

Step 2:            Write out the equation for capacitance

Calculating Capacitance equation 1

Step 3:            Rearrange for charge Q

Q = CV

Step 4:            Substitute in values

Q = (1 × 10-9) × (0.3 × 103) = 3 × 10-7 C = 300 nC

Exam Tip

The letter ‘C’ is used both as the symbol for capacitance as well as the unit of charge (coulombs). Take care not to confuse the two!

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