Chapter 26:  Capacitance and Dielectrics

 

Learning Goals

  1. Know the definition of capacitance.
  2. Know how to calculate capacitance for symmetric arrangements of conductors.
  3. Know how to combine capacitors in series and in parallel.
  4. Understand how energy is stored in capacitors.
  5. Understand how dielectric materials affect capacitors.

 

Capacitance

Two conductors, initially uncharged, will obtain equal and opposite charges Q when a potential difference is applied between them. It is observed the charge Q is always directly proportional to the applied voltage V. The capacitance C is the constant of proportionality:

Q = C V

The units of capacitance are Coulombs/Volt = Farads.

 

Capacitor Combinations

If two or more capacitors are connected in parallel, the potential difference across each capacitor is the same, and

Ceq = C1 + C2 + C3 +...

If two or more capacitors are connected in series, the charge Q is the same for each capacitor, and

 

Energy

The energy stored in a capacitor is

 

Dielectric Materials

Dielectric materials are characterized by a dielectric constant k ³ 1. Filling the space between the capacitor plates with a dielectric material will increase the capacitance by a factor of k:

C = kC0

where C0 is the capacitance without the dielectric.

Dielectric material are composed of molecules with electric dipole moments. In general, a dipole consists of two equal and opposite charges q separated by a distance s. In this case, the electric dipole moment p is given by

P = q s

Electric dipoles in an external electric field E experience a torque given by

The potential energy of such a dipole is given by