3.7.4 Capacitance

3.7.4 Capacitance

1. Capacitance

   • capacitance of a capacitor is the charge stored per unit pd
   • C = Q / V
     • Q = CV
       • V = Q / C

2. Parallel plate capacitor

   • Dielectric action
     • charge stored across plates increased by inserting dielectric between plates
       • examples of dielectric are polythene and waxed paper
     • the molecules of the dielectric become polarised ( electrons pulled slightly towards positive plate and vice versa)
     • as a result more charge is stored on the plates because
       • positive side of the dielectric attracts more electrons from the battery onto the negative plate
       • negative side of the dielectric pushes electrons back to the battery from the positive plate
   • ratio of charge stored with the dielectric to the charge stored without is the relative permittivity, εr of the dielectric substance
     • εr = Q/Q0 = C/C0
   • relative permittivity is also called the dielectric constant
   • C = Aεrε0 / d
     • A is surface area
     • d is spacing between the plates
     • ε0 is permittivity of free space - formula book

3. Energy stored by a capacitor

   • energy stored by capacitor, E = QV/2 = CVV/2 = QQ/2C
     • area under graph of Q against V gives energy stored

4. Capacitor charge and discharge

   • Time constant = RC
   • discharge equation
     • Q=Q0e^(-t/RC)
       • can swap Q for I or V
   • exponential decay curve
   • Time to halve, T1/2 = 0.69RC
   • charging equation
     • Q=Q0(1-e^(-t/RC))