1. Capacitance Physics 102 Professor Lee Carkner Lecture 13

2. PAL #13 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

4. Circuits   A potential difference produces work   Moving charges can do things   Devices are connected to the voltage source in a circuit   Up first, the capacitor

5. Capacitance   Not to be confused with a battery which doesn’t store charge but rather makes charge move   This intrinsic property is called capacitance and is represented by C

6. 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)  One farad equals one coulomb per volt   e.g. microfarad =  F = 1 X 10 -6 F

7. 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

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

9. Capacitor Properties  The capacitance depends on four things:   The distance between them (d)   For air  ~ 1  The permittivity of free space (  0 )  A constant:  0 = 8.85 X 10 -12 C 2 /N m 2  C =  0 (A/d)

10. Capacitance Dependences

11. 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

12. Dielectrics

13. Dielectric Constant   C =  C 0   The dielectric also allows you to move the plates closer together without touching

14. Breakdown   or else the charge would conduct across and not stay separated   Voltage can rip the dielectric’s molecules or atoms apart making it a conductor   The maximum voltage is called the dielectric strength  Normally about 20 million volts

15. 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

16. Charging a Capacitor

17. 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 

18. Using Capacitors   Generally only for short periods of time  Charge can bleed-off if capacitor is not perfectly insulated and potential is not maintained   Defibrillator, flash   Since capacitance depends on d, can also use capacitance to measure separation 

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