Capacitance (DP IB Physics: HL)

• Capacitors are electrical devices used to store energy in electronic circuits, commonly for a backup release of energy if the power fails
• They are in the form of two conductive metal plates connected to a voltage supply (parallel plate capacitor)
  • There is commonly a dielectric in between the plates, this is to ensure charge does not freely flow between the plates

• The capacitor circuit symbol is:

The capacitor circuit symbol is two parallel lines

A capacitor used in small circuits

• Capacitors are marked with a value of their capacitance. This is defined as:

The charge stored per unit potential difference (between the plates)

• The greater the capacitance, the greater the energy stored in the capacitor

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

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

• Capacitance is measured in the unit Farad (F)
  • In practice, 1 F is a very large unit
  • Often it will 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

• This capacitance equation shows that an object’s capacitance is the ratio of the charge stored by the capacitor to the potential difference between the plates

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

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Electric Field in a Parallel Plate Capacitor

• A parallel plate capacitor is made up of two conductive metal plates connected to a voltage supply
  • An assumption made for these types of capacitors is that their length of the plates is much greater than their separation 
• 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

• A dielectric is made up of many polar molecules
  • These are molecules that have a 'positive' and 'negative' end (poles)

• When no charge is applied to the capacitor:
  • There is no electric field between the parallel plates and the molecules are aligned in random directions

• When there is a charge applied:
  • One of the parallel plates becomes positively charged and the other negatively charged hence an electric field is generated between the plates (from positive to negative)
  • The negative ends of the polar molecules are attracted to the positive plate and vice versa
  • This means all the molecules rotate and align themselves parallel to the electric field

Polar molecules align themselves when an electric field is between two parallel plates