Capacitance

Capacitance

1. Discharging

   • Rate of decay of charge is exponential
   • Q=Qoe^(-t/RC)
   • Time Constant (RC), units ohm*farads, or seconds
   • Time Constant is the time at which Q=Qo*e^-1, the charge is 0.37 times the original charge
   • Half life is the time at which the charge has halved
   • Half life = ln(2)RC
   • For a Q against T graph, drawing a tangent from Q at T=0 will give the time constant RC

2. Parallel Plate Capacitors

   • They consist of two parallel conductors separated by a vacuum or a dielectric
   • C= permittivity times area of overlap over seperation
   • Dielectric
     • Must contain molecules which polarise when placed in a magnetic field
     • Reduces the electric field strength meaning a lower p.d. is required, increasing the capacitance
   • Energy stored
     • E=Q^2/2C=1/2CV^2=1/2QV=Area under Q-V graph
   • The Sum of Capacitances
     • In parallel C (total) = C1+C2+C3
     • In series 1/C (total) = 1/C1+1/C2+1/C3

3. Basic Theory

   • C=Q/V
   • Capacitance is how much charge is needed to change the potential by one unit
   • Capacitors are used to store charge

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