7.4 - Capacitance

• How is capacitance calculated?

  C = Q / V

  C = Capacitance (F)

  Q = Charge across the plates (C)

  V = Potential differences across the plates (V)
• What is the relative permittivity also known as?

  The dielectric constant
• What is the relative permittivity?

  - The ratio of the charge stored with the dielectric

  between the plates to the charge stored when the dielectric is not present

  - The greater the relative permittivity, the greater the capacitance of the capacitor

  
• What does the area under the graph of charge against pd represent?

  The energy stored by the capacitor
• Describe the Q against t graph for the discharging of a capacitor through a resistor

  
• Describe the V against t graph for the discharging of a capacitor through a resistor

  
• Describe the I against t graph for the discharging of a capacitor through a resistor

  
• Describe the Q against t graph for the charging of a capacitor through a resistor

  
• Describe the V against t graph for the charging of a capacitor through a resistor

  
• What is the time constant?

  The time it takes for the charge to fall 37% of the initial value, given by t = RC

  A capacitor is considered fully discharged after 5 constants
• How was 37% derived when using the time constant?

  ● Start with the formula Q = Q0 e -t/RC

  ● When t = RC (after 1 time constant), the formula becomes Q = Q0 e -1

  ● e-1 ≈ 0.37, which is where 37% came from.
• What is the half time of a capacitor?

  T½ = 0.69RC
• How does a capacitor charge up?

  1. Electrons move from negative to positive around the circuit.

  2. The electrons are deposited on plate A, making it negatively charged.

  3. Electrons travel from plate B to the positive terminal of the battery, giving the plate a positive charge.

  4. Electrons build up on plate A and an equal amount of electrons are removed from plate B, creating a potential difference across the plates.

  5. When the p.d across plates = source p.d., the capacitor is fully charged and current stops flowing.
• Describe and explain in terms of the movement of electrons how the pd across a capacitor changes, when it discharges across a resistor

  1. Electrons move in the opposite direction than when the capacitor was charging up

  2. Charge on one plate A decreases as it loses electrons, and plate B gains electrons, neutralising them

  3. PD decreases exponentially across the plates
• What 2 factors affect the time taken for a capacitor to charge or discharge?

  - The capacitance of a capacitor (C). This affects the amount of charge that can be stored by the capacitors at any given potential difference across it,

  - The resistance of the circuit (R). This affects the current in the circuit and how quickly it flows, hence how quickly the capacitor charges/discharges