1. 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

2. 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

3. 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.

4. 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

5. 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

6. 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

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

8. 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.

9. 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 ()

10. 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

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

12. 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)

13. Ideal diagrams of “open” and “complete” circuits

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

15. 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

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

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

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

19. Potential Rises and Drops in a Circuit
Figure 25-21

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

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

22. 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

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

24. Power in a Short Circuit
Example 25-11

25. 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

26. A microscopic look at conduction
Consider Figure
Consider Figure
Follow Example