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Announcements. Example. Find the equivalent capacitance of the combination in the figure below. Assume that C 1 = 4 µF, C 2 = 4 µF, and C 3 = 2  µF. What is the equivalent capacitance of the whole system? 10 m F C) 4 m F 1 m F D) 2.5 m F. Example.

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Find the equivalent capacitance of the combination in the

figure below.

Assume that C1 = 4 µF, C2 = 4 µF, and C3 = 2  µF.

  • What is the equivalent capacitance of the whole system?
  • 10 mF C) 4 mF
  • 1 mF D) 2.5 mF


In the figure below the battery has a potential difference of 10 V

and the five capacitors each have a capacitance of 12 µF.

What is the charge on capacitor C1?

What is the charge on capacitor C2?


Capacitors and Dielectrics

Dielectric constant 

area A

  • A dielectric changes the capacitance
  • Cause a breakdown potential, Vmax to exist.


  • Beyond the breakdown potential the dielectric starts to conduct!

Capacitors and Dielectrics





  • Charges are aligned and/or induced in the diectric
  • Remember the in-class concept quiz
  • The charge alignment reduces the field!
gauss law with a dielectric
Gauss’ law with a dielectric

Original formulation:

Flux is proportional to the charge

More General formulation:

The integral of the

electric displacement equals the charge


Coulomb’s Law with a dielectric

  • Original formulation
  • In the presence of a dielectric
dielectrics and dipoles
Dielectrics and Dipoles

When a dielectric is placed inside a capacitor, it is polarized

That is the dipole moments of polar molecules partially align

Nonpolar molecules have dipoles induced and partially aligned

Surface charges are created and fields generated (e. g. induced) which

lowers the field inside the capacitor, and hence reduces the potential

difference and raises the capacitance.

types of electric dipoles







CO2 and water



Types of Electric Dipoles

There are two types of dipoles:

Permanent dipoles (always a charge separation):


Temporary Dipoles: (Induced Dipoles):


Charging of Capacitors




  • The instantaneous charge is q, so the instantaneous potential difference is q/C
  • Work is required to move charge through a potential difference
  • Work is required to put charge
  • Q on a capacitor
  • This work becomes potential energy stored in the capacitor

area A


Energy Density

Dielectric constant 


Energy Density

We say there is an energy density,

Note: the final energy density does not

depend on anything to do with the capacitor!

This energy density is actually the energy density of an

electric field. This is why we care about the energy density.


Overview of Capacitors

  • Capacitors accumulate separated charge
  • Capacitance is measure of how well a capacitor stores charge.
  • Farad (F) is C/V, measures capacitance
  • Typical capacitances measured in mF,F or pF
  • Capacitors also store energy
  • The capacitance depends on the geometry of the capacitor and the
  • presence or absence of a dielectric medium .