1. Capacitance Physics 102 Professor Lee Carkner Lecture 13

2. PAL #12 Electric Potential sign of  U sign of  V sign of Wnaturally? + charge moves with E field + charge moves against E field -charge moves with E field -charge moves against E field - - - - - - + + + + + + Yes No

3. Particle Motion E Low V High V Increase U Decrease U (natural) Decrease U (natural)

4. If a charge of value Q is at a point of potential V, we know, A)The velocity of the charge at that point B)The direction the charge will move in C)The amount of electrical potential energy the charge has D)The distance to the nearest other charge E)None of the above

5. If a charged particle moves along an equipotential line (assuming no other forces), A)Its potential energy does not change B)No work is done C)Its kinetic energy does not change D)Its velocity does not change E)All of the above

6. When a charge +Q is placed at the corner of a square the potential at the center is 3 volts. What is the potential at the center if charges of +Q are placed on all corners of the square? A)0 V B)3 V C)9 V D)12 V E)24 V

7. Circuits  What is the purpose of potential difference?   It makes charges move   e.g. light lightbulbs, induce movement in motors, move information etc.   We will examine the key components of electric circuits  Up first, the capacitor

8. Capacitance  A capacitor is a device that can store charge and thus energy   The amount of charge depends on the potential difference across the capacitor and the intrinsic properties of the device  This intrinsic property is called capacitance and is represented by C

9. Capacitance Defined  The amount of charge stored by a capacitor is just:  Or, defining the capacitance: C = Q/  V   The units of capacitance are farads (F) 1 F = 1 C/V   Typical capacitances are much less than a farad:  e.g. microfarad =  F = 1 X 10 -6 F

10. Capacitor Info   Maintaining a potential difference across the plates causes the charge to separate   Electrons are repelled from the negative terminal and end up on one plate   Plates have a net charge  Plates can’t touch or charge would jump across

11. Capacitor Diagram - - ++ VV VVQ

12. Capacitor Properties  The capacitance depends on four things:   The distance between them (d)  The dielectric constant of the material between the plates (  )   The permittivity of free space (  0 )  A constant:  0 = 8.85 X 10 -12 C 2 /N m 2  The total capacitance can be written as: C =  0 (A/d)

13. Capacitance Dependences

14. Dielectric   The molecules in the material will align with the electric field   The polarized material partially cancels out the electric field between the plates reducing the voltage   A dielectric allows a capacitor to store more charge with the same voltage

15. Dielectrics

16. Dielectric Constant  The dielectric constant is a multiplicative factor for the capacitance  C =  C 0  e.g.  The dielectric also allows you to move the plates closer together without touching

17. Breakdown  The dielectric must be an insulator   If the voltage is large enough, the charge will jump across anyway   While Q = CV, there is a limit to how much we can increase Q by increasing V   Normally about 20 million volts

18. Energy in a Capacitor   Every little batch of charge increases the potential difference between the plates and increases the work to move the next batch   Charge stops moving when the  V across the plates is equal to the max  V possible for the circuit

19. Charging a Capacitor

20. Total Energy  We find that the total energy stored in a capacitor is related to the charge and the final potential difference: Energy = 1/2 Q  V =1/2 C (  V) 2 = Q 2 /2C   Large C and large  V produce large stored energy 

21. Using Capacitors   Generally only for short periods of time  Charge can bleed-off if capacitor is not perfectly insulated and potential is not maintained  Useful when you need a quick burst of energy   For a flash, capacitor is discharged into a gas (like xenon) that will glow when ionized  Since capacitance depends on d, can also use capacitance to measure separation 

22. Next Time  Read 18.1-18.5, 18.8-18.9  Homework Ch 17, P: 44, 49, Ch 18, P: 4, 26