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
- 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):
- Substituting this into the capacitance equation means the capacitance C of a sphere is given by the expression:
C = 4πε0r
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
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!