1. Capacitors PH 203 Professor Lee Carkner Lecture 8

2. Circuits   A potential difference produces work   Moving charges can do things  e.g. light lightbulbs, induce movement in motors, move information etc.   We will examine the key components of electric circuits  Up first, the capacitor

3. Battery  The source of potential difference in a direct current (DC) circuit is a battery   If we connect one end of a wire to the positive terminal and the other end to the negative terminal, the electrons in the wire will move   often called a voltage   it just provides the potential to move the electrons that are already in the wire + -

4. 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

5. Capacitance Defined  The amount of charge stored by a capacitor is just: Q = C  V  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

6. Simple Circuit  Battery (  V) connected to capacitor (C)   The capacitor experiences potential difference of  V and has stored charge of Q = C  V +- + - VV C Q

7. Connections  When connecting things to a battery the arrangement can be in series or parallel  Series   with potential source connected to each end of line   Parallel   each element has the same potential VV 123 V 1 + V 2 + V 3 =  V VV 1 2 3 V 1 = V 2 = V 3 =  V

8. Junctions  How can you tell if capacitors are in series or parallel?   A place where the current has to split   If you can’t draw a path from one capacitor to the other without hitting a junction, they are in parallel +- VV C1C1 C2C2

9. Capacitors in Parallel  Potential difference across each is the same (  V)  Total stored charge is the sum (Q = Q 1 + Q 2 )  But:    Q = C eq  V   C eq = C 1 + C 2 +- VV C1C1 C2C2

10. Capacitors in Series  Charge stored by each is the same (Q)  Equivalent capacitor also has a charge of Q   Since  V = Q/C:   The equivalent capacitance is:  1/C eq = 1/C 1 + 1/C 2 +- VV C1C1 C2C2 + -- +

11. Capacitors in Circuits  Remember series and parallel rules extend to any number of capacitors   Keep simplifying until you find the equivalent capacitance for the whole circuit

12. Capacitor Info  A capacitor generally consists of two metal surfaces   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  Electrons are attracted to the positive terminal and are lost by the second plate   Plates can’t touch or charge would jump across

13. Finding Capacitance  We will enclose one plate with a Gaussian surface   But for the special case of our capacitors:  The plate has a charge q   Thus EA = q/  0 q =  0 EA   q = CV =  0 EA  C =  0 EA/V

14. Parallel Plate  What is the relation between E and V for two parallel plates?  But E is constant between the plates and ∫ ds = d, the distance between the plates C =  0 A/d

15. Capacitor Properties  What kinds of capacitors can hold a lot of charge?   Very close together (small d)   0 = Cd/A   So we can write:  0 = 8.85 X 10 -12 F/m  and think of  0 as being the “capacitor constant”

16. Using Capacitors  Capacitors store energy  Generally only for short periods of time   Useful when you need a quick burst of energy  Defibrillator, flash   Since capacitance depends on d, can also use capacitance to measure separation 

17. Next Time  Read 25.5-25.8  Problems: Ch 25, P: 6, 9, 14, 26, 36

18. A)0 B)1 C)√2 D)4 E)You cannot tell without knowing the value of “a” If the potential at the center of the square from charge A is 1, what is the net potential from all the charges at the center of the square? A

19. A)You would have to do positive work B)The work would equal zero C)You would do “negative work”, the charge would move in on its own D)The work would first be positive, then negative E)You cannot tell without knowing the value of “a” If the other three charges were already fixed in place, how much work would you have to do to bring charge A into place from infinity? A