Capacitance (CIE A Level Physics)

• Capacitors are electrical devices used to store charge
  • In electronic circuits, they are commonly used as a backup store of energy in case of power failure

• The circuit symbol for a parallel plate capacitor is two parallel lines

Capacitor circuit symbol

The circuit symbol for a capacitor consists of two parallel lines perpendicular to the wires on either side  

• Capacitors possess capacitance, which is defined as:

The charge stored per unit potential

• The greater the capacitance, the greater the charge stored on the capacitor

• Capacitors come in different forms, such as:
  
  • isolated spherical conductors
  • parallel plates

Isolated spherical conductors

• An isolated spherical conductor can store charge on its surface, which means it can act as a capacitor
• When the conducting sphere is connected to a high-voltage supply:
  • electrons move on to, or off of, the surface of the sphere 
  • the remaining charges are of the same type, so they repel
  • the surface is conducting, allowing them to move and become evenly distributed

• As the potential difference of the supply increases, the charge on the conductor also increases
• The capacitance of the sphere is equal to the ratio of the charge to the potential

Parallel plate capacitors

• A parallel plate capacitor is made up of two conducting 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 a dielectric between the plates which ensures charge does not flow freely between the plates

Capacitance of a parallel plate capacitor

A parallel plate capacitor is made up of two conductive plates with opposite charges building up on each plate

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

• Where:
  • C = capacitance (F)
  • Q = charge (C)
  • V = potential difference (V)

• The unit of capacitance is the farad (F), where one farad is equivalent to one coulomb per volt
  
  • In practice, 1 F, or 1 C V^–1, is a very large unit
  • As a result, capacitance values are often quoted in microfarads (μF), nanofarads (nF) or picofarads (pF)

A typical capacitor

A capacitor of capacitance 47 μF might typically be used in a simple circuit

• For a parallel plate conductor, Q is the charge on the plates and V is the potential difference across the capacitor
  • Note: The charge Q is not the charge of the capacitor itself, it is the charge stored on the plates

• 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 an isolated spherical conductor is equal to the charge per unit potential at the surface of the sphere
  • This is because the charge on the surface of a spherical conductor can be considered as a point charge at its centre

• The potential V of an isolated point charge is given by:

• Where:
  • R = radius of the sphere (m)
  • ε₀ = permittivity of free space

• Combining these equations gives an expression for the capacitance of an isolated spherical conductor:

C = 4πε₀R

• Note: The charge Q is not the charge of the capacitor itself, it is the charge stored on the surface of the spherical conductor