Chapter 25 Current, Resistance, Electromotive Force Consider current and current density Study the intrinsic property of resistivity Use Ohm’s Law and study resistance and resistors Connect circuits and find emf Examine circuits and determine the energy and power in them Describe the conduction of metals microscopically, on an atomic scale

The direction of current flow In the absence of an external field, electrons move randomly in a conductor. If a field exists near the conductor, its force on the electron imposes a drift. -The electrons move at a random velocity and collide with stationary ions. Velocity in the order of 106 m/s -Drift velocity is approximately 10-4 m/s

Current flowing Positive charges would move with the electric field, electrons move in opposition. The motion of electrons in a wire is analogous to water coursing through a river.

Electric Current (25-1) Conventional Current Direction Electrical current (I) in amperes is defined as the rate of electric charge flow in coulombs per second. 1 ampere (A) of current is a rate of charge flow of 1 coulomb/second. 1 mA (milliampere) = 1 x 10-3 A (ampere) (25-1) 1 A(microampere) = 1 x 10-6 A (ampere) Conventional Current Direction Chapter 25

Electric Current Density Current, Drift Velocity, and Current Density where n = charge carriers per unit volume q = charge per charge carrier in coulombs vd = average drift velocity of charge carriers in meters per second amperes = current density in amperes/m2 Chapter 25

Resistivity Definition of resistivity in ohm-meters (-m). where Drift Velocity where  = mobility of conducting material Drift Velocity is 1010 slower than Random Velocity Definition of resistivity in ohm-meters (-m). where conductivity of the material. Resistivity of the material. Chapter 25

Resistivity is intrinsic to a metal sample (like density is)

Resistivity and Temperature In metals, increasing temperature increases ion vibration amplitudes, increasing collisions and reducing current flow. This produces a positive temperature coefficient. In semiconductors, increasing temperature “shakes loose” more electrons, increasing mobility and increasing current flow. This produces a negative temperature coefficient. Superconductors, behave like metals until a phase transition temperature is reached. At lower temperatures R=0.

Resistance Defined – + Ohm’s Law therefore for a uniform E – Solve for V + therefore Ohm’s Law where R is the resistance of the material in ohms ()

Ohm’s law an idealized model If current density J is nearly proportional to electric field E ratio E/J = constant and Ohm’s law applies V = I R Ohm’s Law is linear, but current flow through other devices may not be. Linear Nonlinear Nonlinear Ohm’s law applies

Resistors are color-coded for assembly work Examples: Brown-Black-Red-Gold = 1000 ohms +5% to -5% Yellow-Violet-Orange-Silver = 47000 ohms +10% to -10%

Electromotive force and circuits If an electric field is produced in a conductor without a complete circuit, current flows for only a very short time. An external source is needed to produce a net electric field in a conductor. This source is an electromotive force, emf , “ee-em-eff”, (1V = 1 J/C)

Ideal diagrams of “open” and “complete” circuits

Symbols for circuit diagrams Shorthand symbols are in use for all wiring components

Electromotive Force and Circuits Electromotive Force (EMF) Ideal Source I Complete path needed for current (I) to flow Voltage rise in current direction + + VR – Voltage drop in current direction – Ideal source of electrical energy VR = EMF = R I Real Source I a + External resistance Internal source resistance + Vab – – Real source of electrical energy b

A Source with an Open Circuit Example 25-5 I = 0 amps Figure 25-16 Chapter 25

A source in a complete circuit Example 25-6 Figure 25-17

A Source with a Short Circuit Example 25-8 I = 6 A Figure 25-19 Chapter 25

Potential Rises and Drops in a Circuit Figure 25-21

Energy and Power Pure Resistance 1 watt = 1 joule/sec Defined Substitute for Divide by watts Pure Resistance 1 watt = 1 joule/sec

Power Output of an EMF Source I a + – + + Vab – – b Power output of battery Power dissipated in R Power dissipated in battery resistance Power supplied by the battery Chapter 25

Power Input to a Source – + Vab greater then the EMF of the battery + Power dissipated in battery resistance Power charging the battery Total Power input to battery

Power Input and Output in a Complete Circuit Example 25-9 Figure 25-25

Power in a Short Circuit Example 25-11

Theory of Metallic Conduction Simple, non-quantum-mechanical model Each atom in a metal crystal gives up one or more electrons that are free to move in the crystal. The electrons move at a random velocity and collide with stationary ions. Velocity in the order of 106 m/s (drift velocity is approximately 10-4 m/s) The average time between collisions is the mean free time, τ. As temperature increases the ions vibrate more and produce more collisions, reducing τ. Chapter 25

A microscopic look at conduction Consider Figure 25.27. Consider Figure 25.28. Follow Example 25.12.