CIE A Level Physics复习笔记19.1.1 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

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)
• 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