C  0 AdC  0 Ad C Q VC Q V Capacitors:Store Electric Energy To calculate: 1)Put on arbitrary ±Q 2)Calculate E 3)Calculate  V Parallel Plate Capacitor: P8 -

Batteries & Elementary Circuits P8 - 2

Ideal Battery Fixes potential difference between its terminals Sources as much charge as necessary to do so Think:Makes a mountain P8 - 3

Batteries in Series V1V1 P8 - 4 V2V2 Net voltage change is  V =  V 1 +  V 2 Think: Two Mountains Stacked

BatteriesinParallel Net voltage still  V Don’t do this! P8 - 5

Capacitors in Parallel P8 - 6

Capacitors in Parallel Same potential! C  Q 1,C  Q 2 1  V 2  V P8 - 7

Equivalent Capacitance ? Q  Q 1  Q 2  C 1  V  C 2  V   C 1  C 2   V C  Q  C  C 12eq VV P8 - 8

CapacitorsinSeries Different Voltages Now What about Q? P8 - 9

CapacitorsinSeries P8 - 10

Equivalent Capacitance 1212 C1C2C1C2 V Q,V QV Q,V Q  V   V 1   V 2 (voltage adds in series)  V  Q  Q  Q C1C2C1C2 C eq C1C2C1C2 1  1  1 C eq P8 - 11

PRS Question: Capacitors in Series and Parallel When capacitors are combined, they behave in an opposite way comparing to resistors. P8 - 13

Dielectrics P A dielectric is a non-conductor or insulator Examples: rubber, glass, waxed paper When placed in a charged capacitor, the dielectric reduces the potential difference between the two plates HOW???

Molecular View of Dielectrics Polar Dielectrics : Dielectrics with permanent electric dipole moments Example: Water P8 - 15

Molecular View of Dielectrics Non-Polar Dielectrics Dielectrics with induced electric dipole moments Example: CH 4 P8 - 16

Dielectric in Capacitor Potential difference decreases because dielectric polarization decreases Electric Field! P8 - 17

Gauss’sLawforDielectrics Upon inserting dielectric, a charge density  ’ is induced at its surface 0000   S inside q E  dA  EA E  dA  EA   E     '0E     '0    ' A   ' A P  What is  ’?

Dielectric Constant  Dielectric weakens original field by a factor  E     '  E0 0E     '  E0 0 00   '   1 1  '   1 1  P Bound charge = free charge (1-1/  Total net charge = free charge – bound charge = free charge/ 

Dielectric Constant  Dielectric weakens original field by a factor  Very often, people use  instead of  to  represent dielectric constant. Dielectric constants P Vacuum1.0 Paper3.7 Pyrex Glass5.6 Water80 For a vacuum(air)-filled capacitor For a dielectric-filled capacitor  for vacuum.  for other insulators (dielectrics).

Dielectric in a Capacitor Q 0 = constant after battery is disconnected  Upon inserting a dielectric: Q0Q0   Q0 C  Q0 C 0 00 C  Q VV/ C  Q VV/  V P Dielectric filling will increase C by a factor of  when free charge Q is unchanged, E field and  V will reduce by a factor of  E and V reduces due to bounded charges.

Dielectric in a Capacitor V 0 = constant when battery remains connected Upon inserting a dielectric: Q   Q 0 C  Q   C  Q0C  Q   C  Q0 P V0V0 V Dielectric filling increases C by a factor of  When  V  is constant, Q increase by a factor of 

PRS Questions: Dielectric in a Capacitor P8 - 23

Capacitors & Dielectrics To calculate: 1)Put on arbitrary ±Q 2)Calculate E 3)Calculate  V C QC Q  V V Energy 2 Capacitance Q 12C2Q 12C2 C VC V P10 - Q VQ V U U  o E EE udrudr drdr  Dielectrics When  V is fixed, adding dielectric filling increases U by a factor of . When Q (free charge) is unchanged, adding dielectric filling decreases U by a factor of .

For a vacuum(air)-filled capacitor Q 12C2Q 12C2 C VC V Q VQ V U U  3 E udr= u E Ad  For a dielectric-filled capacitor