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Chapter 20

Chapter 20. Circuits. 1) Electric current and emf. Potential difference and charge flow Battery produces potential difference causing flow of charge in conductor. b) Current: I = D q/ D t. ∆ q is charge that passes the surface in time ∆ t. Units: C/s = ampere = A.

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Chapter 20

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  1. Chapter 20 Circuits

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

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

  4. Drift velocity: average velocity of electrons ~ mm/s • Signal velocity: speed of electric field = speed of light in the material ~108 m/s

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

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

  7. R • Real battery E r Battery terminals V < Ein general

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

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

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

  11. A L 3) Resistivity a) Definition • 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

  12. b) values • Conductors: r ~ 10-8 Wm (Cu, Ag best) • Semiconductors: r ~ 1 - 103 Wm (Ge, Si) • Insulators: r ~ 1011 - 1016Wm (rubber, mica)

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

  14. d) Superconductors • Below critical temp Tc, r –> 0 • Current flows in loop indefinitely • Quantum transitions not possible Tc typically < 10 K, but can be > ~ 75 K (high Tc ceramics) (record is 138 K) Applications: MRI, MagLev trains

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

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

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

  18. V0 V t -V0 I V ac generator alternates polarity: b) Alternating Current

  19. V0 V I0 t -V0 I t -I0 For resistors Average power: Average voltage: zero Average current: zero

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

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

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

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

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

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

  26. I R1=6 V=10V Vo R2=4 V Vo Voltage divider Current is the same in both resistors Voltages divide in proportion to R Output Voltage:

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

  28. In general, for parallel resistors, or • Equivalent resistance is smaller than either R1 or R2 • Conductance adds

  29. conductance adds

  30. parallel connections in the home

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

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