Capcitors

• Capacitor


  A component that stores charge
• Capacitance


  The charge stored per unit potential difference
• Equation for capacitance


  1. C = Q/V

  2. Where C is capacitance, Q is charge and V is potential difference
• Charge-voltage graph


  • Gradient represents capacitance
  • Area represents energy stored
• Equation for energy stored by a capacitor


  E = ½ QV
• Time constant of a capacitor

  The time it takes for a capacitor to charge to 63% of its total charge or the time taken for a capacitor to discharge to 37% of its initial value
• Equation for time constant of a capacitor

  Time Constant = Resistance x Capacitance
• Capacitor


  A circuit component which stores charge. It consists of two plates on which charge builds up. Electrons flow across the circuit from one plate to the other, building up opposite charges.
• Capacitance, C


  The charge separated/stored per volt
• Energy stored on a capacitor

  E = 1/2 QV
• On a graph of Q against V

  The capacitance is equal to the gradient and the energy is equal to the area under the graph
• Time constant (RC)

  The product of the resistance and capacitance of a circuit
• Time constant, τ


  The time (in s) taken for the charge stored on a discharging capacitor to drop to 37% of its original value, or for a charging capacitor to charge to 63%. This is the value of 1/e
• Capacitors can also be modelled with iterative methods


  dQ/dt = -Q/RC
• Discharging


  1. Q = Q0e^(-t/RC)

  2. V = V0e^(-t/RC)

  3. I = I0e^(-t/RC)