1. 1 25 Overview electric current & circuits Ohm’s Law energy Kirchoff’s Rules RC circuits

2. 2 Current: Charge Flow I = Q/t (coulomb/second = ampere, A) affected by material and field carriers: electrons or “holes”

3. 3 current parameters q = charge/carrier n = carriers/volume A = cross-section vd = drift velocity

4. 4 Conductors F = qE moves charges  V = -E  L Vb < Va

5. 5 Electrical Resistance ohm,  [volt/amp] Example: 6.0V causes 0.1A current:

6. 6 Ohm’s Law many materials have constant V/I e.g. 2V causes 2I (2V/2I = V/I) called “Ohmic” Ohmic Non- Ohmic

7. 7 Example Non-Ohmic: Diode Sizeable current flows in only one direction

8. 8 Example Diode Application Half-Wave Rectifier Full-Wave Rectifier

9. 9 Resistivity “specific resistance” Intrinsic (does not depend on shape) Resistance is Extrinsic (depends on shape) Symbol:  (“rho”). SI Unit: ohm-meter (  -m)

10. 10 Factors Affecting Resistivity Temperature Defects Impurities

11. 11 some resistivities @ 20C n  m  m silver16 copper 17 aluminum28 nichrome1000 silicon640 insulators10 8 to 10 16

12. 12 Resistance & Resistivity where is the “Shape-Factor” Example: R = 3ohms, L = 15m, A = 10 -6 m 2

13. 13 Energy Dissipated in a Resistor

14. 14 Circuit Analogy

15. 15 “Terminal Voltage” Real Battery internal battery resistance load resistor

16. 16 Combinations of Resistors

17. 17 Connection Types Series Parallel

18. 18 Equivalent Resistances Series Parallel Ex. R1 = 4, R2 = 12: Req = 4 + 12 = 16 ohms Ex. R1 = 4, R2 = 12: Req = (4 -1 + 12 -1 ) -1 = 3 ohms

19. 19 Ex. Calc: equivalent resistance, current, voltages, powers dissipated

20. 20 Ex. Calc: equivalent resistance, current, voltages, powers dissipated

21. 21 Calc: equivalent resistance

22. 22 Kirchhoff’s Rules

23. 23 Kirchoff’s Rules: 1.Loop Rule. 2.Junction Rule.

24. 24 I1I2 I I = I1 + I2 (junction) a b a b

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26. 26 Calc: I = 2A, I2 = 0.5A, I1 = 1.5A

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28. 28 Ammeter: small r (Req = R)

29. 29 Voltmeter: large r (Req = R)

30. 30 RC Circuits

31. 31 Charging/Discharging C’s Resistance affects time required Capacitance value also affects time needed time constant = RC. Benchmarks values related to e = 2.718 discharge: 1/e = 0.3678, Q @ t = RC charge: 1 – 1/e = 0.6321, Q @ t = RC

32. 32 Summary electric current is + flow of charge/time V = IR R =  L/A P = I 2 R circuits obey charge and energy cons. RC = exponential time constant

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