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

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

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

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

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

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

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

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

10 Factors Affecting Resistivity Temperature Defects Impurities

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

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

13 Energy Dissipated in a Resistor

14 Circuit Analogy

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

16 Combinations of Resistors

17 Connection Types Series Parallel

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

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

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

21 Calc: equivalent resistance

22 Kirchhoff’s Rules

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

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

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

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28 Ammeter: small r (Req = R)

29 Voltmeter: large r (Req = R)

30 RC Circuits

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

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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