1. 1 Chapter 20 Circuits

2. 2 1) Electric current and emf a)Potential difference and charge flow Battery produces potential difference causing flow of charge in conductor

3. 3 b) Current: I =  q/  t ∆ q is charge that passes the surface in time ∆ t Units: C/s = ampere = A

4. 4 Drift velocity: average velocity of electrons ~ mm/s Signal velocity: speed of electric field = speed of light in the material ~10 8 m/s

5. 5 emf = electromotive force = maximum potential difference produced by a device Symbol: E emf is not a force, but it causes current to flow E  is like gh c) Electromotive force, emf gravitational analogy for a circuit battery

6. 6 Symbol for a perfect seat of emf E V = E

7. 7 Real battery r R V < E  in general Battery terminals E

8. 8 2) Ohm’s Law Ohm’s law: for some devices (conductors), I is proportional to V: I V Device I V V = IR R = Resistance = proportionality constant = V/I

9. 9 Current depends on voltage I V Device I V I VV I and on the device Resistance R = V / I, not necessarily constant

10. 10 Ohmic material obeys Ohm’s Law: R is constant R is a property of the device I V Device symbol:

11. 11 3) Resistivity Property of material; zero for superconductors For cylindrical conductor: R is proportional to L R is proportional to 1/A R is proportional to L / A Define resistivity  as the proportionality constant a) Definition A L

12. 12 b) values Conductors:  ~ 10 -8  m (Cu, Ag best) Semiconductors:  ~ 1 - 10 3  m (Ge, Si) Insulators:  ~ 10 11 - 10 16  m (rubber, mica)

13. 13 c) Temperature dependence Resistivity is linear with temperature: For metals,  > 0 (resistance increases with temp) For semiconductors,  < 0 (resistance decreases)

14. 14 d) Superconductors Below critical temp T c,  –> 0 –Current flows in loop indefinitely –Quantum transitions not possible T c typically ~ 75 K (high Tc ceramics) (record is 138 K) Applications: MRI, MagLev trains

15. 15 4) Power and Energy Energy lost or gained by  q is  U  qV Power: V I Units: (C/s)(J/C) = J/s = W Consumed energy = P t: [kW h] = (1000 W) (3600 s) = 3.6 MJ a) Power dissipated in a device

16. 16 b) Power dissipated in resistors V I V = IR

17. 17 6) AC/DC a) Direct (Constant) Current I V V t

18. 18 b) Alternating Current V I t V0V0 -V 0 V ac generator alternates polarity:

19. 19 Average voltage: zero t V0V0 -V 0 V t I0I0 -I 0 I Average current: zero Average power: For resistors

20. 20 6) Circuit wiring a) Basic circuit I E

21. 21 b) Ground One point may be referred to as ground I E The ground may be connected to “true” ground through water pipes, for example. I E =

22. 22 d) Open circuit E I c) Short circuit E

23. 23 f) Parallel connection e) Series connection same current I same voltage V

24. 24 7) Resistors in series For perfect conductors From Ohm’s law if

25. 25 In general, for series resistors, Find the current and the power through each resistor.

26. 26 Voltage divider V=10V R 1 =6  R 2 =4  Current is the same in both resistors I Voltages divide in proportion to R VoVo Output Voltage: V VoVo

27. 27 8) Resistors in parallel a) General case Conservation of charge Ohm’s Law if

28. 28 Equivalent resistance is smaller than either R 1 or R 2 Conductance adds In general, for parallel resistors, or

29. 29 conductance adds

30. 30 parallel connections in the home

31. 31 b) Special cases i) Equal resistance ii) Very unequal resistors (e.g. 1  and 1 M  R P = the smaller value