# 19.1.1 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

• 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! ### Author: Katie

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.
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