Chapter 26 Current Resistance and Electromotive Force Charge

Chapter 26: Current, Resistance and Electromotive Force Charge carrier motion in a conductor in two parts Constant Acceleration Randomizing Collisions (momentum, energy) =>Resulting Motion Average motion = Drift Velocity = vd ~10 -4 m/s Typical speeds ~ 106 m/s p 212 c 26: 1

Current Flow = net motion of charges = Charge carriers charge q speed vd vd I I = Current = rate at which charge passes the area vd I Negative charge carriers move in opposite direction of conventional current. p 212 c 26: 2

Connection with microscopic picture: E q A vd d. Q = charge that passes through A = number that pass through A ´ charge on each = (n A vd dt) q, n = number density = number/volume Current Density: (works for negative charge carriers, multiple types of charge carriers as well) p 212 c 26: 3

Example: 18 gauge copper wire (~1. 02 mm in diameter) -constant current of 2 A -n = 8. 5 x 1028 m-3 (property of copper) find J, vd p 212 c 26: 4

Current as a response to an applied electric field p 212 c 26: 5

J J slope = 1/r J E linear response Ohm’s Law E nonlinear response E diode nonlinear response direction dependence! r depends upon • material • E • Temperature If r does not depend on E, the material is said to obey “Ohm’s Law” p 212 c 26: 6

For a cylindrical conductor E J I a b see also example 28 -3 re: alternate geometries Example: 50 meter length of 18 gauge copper wire (~1. 02 mm in diameter) constant current of 2 A r = 1. 72 x 10 -8 W. m find E, V, R p 212 c 26: 7

Temperature Dependence of r r r T Metallic Conductor r T Semiconductor T Superconductor For small changes in temperature: p 212 c 26: 8

Resistor Color Codes Color number black 0 brown 1 red 2 orange 3 yellow 4 green 5 blue 6 violet 7 gray 8 white 9 color range none ± 20% silver ± 10% gold ± 5% value: n 1 n 2 x 10 n 3±x% 10 x 102± 5% p 212 c 26: 9

Electromotive Force and Circuits Steady current requires a complete circuit path cannot be only resistance cannot be only potential drops in direction of current flow Electromotive Force (EMF) provides increase in potential E converts some external form of energy into electrical energy Single emf and a single resistor: V = IR I + - V = IR = E E p 212 c 26: 10

Measurements Voltmeters measure Potential Difference (or voltage) across a device by being placed in parallel with the device. V Ammeters measure current through a device by being placed in series with the device. A p 212 c 26: 11

Real Sources and Internal Resistance E a r b Ideal emf E determined by how energy is converted into electrical energy Internal Resistance r unavoidable “internal” losses aging batteries => increasing internal resistance p 212 c 26: 12

Open Circuit I=0 Vr=0 Vab= E V r E a A b V Short Circuit Vr = Ir = E Vab= 0 E a r b A p 212 c 26: 13

V Complete Circuit r E a b I A R Charging Battery V I A E a r b p 212 c 26: 14

Energy and a Power I + V=IR b a + - b V= E p 212 c 26: 15

Power and Real Sources E Discharging Battery I a E Charging Battery I r a b I r p 212 c 26: 16

Real Battery with Load V E r a b A I R p 212 c 26: 17

Complete Circuit Example V E =12 V r = 2 W a b A R = 4 W p 212 c 26: 18

Theory of Metallic Conduction Constant Acceleration between randomizing collisions (momentum, velocity randomized) p 212 c 26: 19

Example: What is the mean time between collisions and the mean free path for conduction electrons in copper? p 212 c 26: 20

Physiological Effects of Current Nerve action involves electrical pulses currents can interfere with nervous system ~. 1 A can interfere with essential functions (heartbeat, e. g. ) currents can cause involuntary convulsive muscle action ~. 01 A Joule Heating (I 2 R) With skin resistance dry skin: R ~ 500 k. W wet skin: R ~ 1000 W p 212 c 26: 21