Knowledge-16 C

• A capacitor is a device designed to store charge.
• The capacitance C of a capacitor is the charged stored per unit potential difference:

  • C = Q/V
• 1 farad is a large capacitance so it is common to see capacitors labelled in microfarads.
• A simple capacitor consists of two parallel metal plates opposite each other with a gap between them.
• The energy stored in a charge capacitor can be calculated using:

  • E = 1/2 QV = 1/2 CV^2 = 1/2 Q^2 /c
• The energy stored by a charged capacitor is equal to the area under the chance against p.d graph or the p.d against charge graph.
• The energy supplied to charge up a capacitor is:

  • E = QV
• The energy stored by the capacitor is half of E =QV because the rest of energy is lost to the resistance of the circuit and the internal resistance of the power supply.
• the charge stored on the plates of a capacitor can be increased by inserting a dielectric between the plates.
• the relative permittivity of a dielectric is the ratio of charge stored with the dielectric to the charge stored without a dielectric.

  • E = C/C0 = Q/Q0 = E/E0
• Dielectrics increase the capacitance of a capacitor by:

  • dielectrics contain polar molecules that align themselves with the electric field between the plates.
  • this causes an electric field that partially cancels the electric field caused by the charges against the plate.
  • This reduces p.d across the capacitor meaning more charge can be stored per volt.
• Parallel plate capacitor:

  for a parallel plate capacitor with a dielectric between plates the capacitance is :

  • C = A e0 er / d
• Graphs of current against time for the discharging of a capacitor show an exponential decay.
• The area under the current-time graph is equal to the charge that has flowed off the capacitor. The gradient of the tangent of the charge-time graph at any point is equal to the current at that time.
• The time constant for a capacitor discharge circuit is :

  • time constant = RC
  • RC is the time taken for the charge , current and p.d to fall to 1/e of its original value.
  • 5RC is a good approximation of the time taken to fully discharge a capacitor.
• the time constant is equal to -1/gradient of the graphs of ln V,Q,I against time.
• The half-life of a capacitor discharge circuit is the time take for the charge , current and p.d to fall to halve.

  • T (1/2) = 0.69RC
• Relative permittivity is the ratio of charge stored with the dielectric between plates compared to the charge stored without the dielectric.
• The area underneath a graph of charge against p.d represents the energy stored by the capacitor
• The time constant is the time it takes for the charge in a capacitor to fall to 37% of the initial values. A capacitor is seen as fully discharged after 5 time constants.
• To derive 37%:

  • start with the Q = Q0 x e ^ (-t /rc)
  • T = RC after one time constant
  • Q=Q0 x e^ -1
  • e^-1 is 0.37 hence 37%
• The half life of a capacitor is 0.69RC
• How does a capacitor charge:

  1. electrons move from negative to positive around a circuit.
  2. The electrons are deposited on plate A making them negatively charged.
  3. Electrons travel from plate B to the positive terminal of the battery , generating a positive charge on the plate.
  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 p.d across plate = p.d source the capacitor is charged.
• movement of electrons across a capacitor when it discharges across a resistor:

  1. Electrons move in an opposite direction compared to when the capacitor was charging up.
  2. Charge on one plate A decreases as it loses electrons , plate B gains electrons neutralizing them.
  3. P.d decreases exponentially across the plates.
• Two factors that affect time taken for capacitor to charge or discharge:

  1. the capacitance - this affects the amount of charge that can be stored by the capacitors at any given p.d across it.
  2. The resistance of the circuit and how quickly it flows , hence how quickly the capacitor charges/ discharges.