Current, Resistance andElectromotive Force

Young and FreedmanChapter 25

Electric Current: Analogy, water flowing in a pipe

H20gallons/minute

Individual molecules arebouncing around withspeeds of km/s!

Net water velocity is m/s

ICoulombs/s

Individual electrons arebouncing around withvery high speed

Electron “drift velocitymay be mm/s

- -

--

--

--

---

--

--

“Flow Rate” is the NET amountof water passing through asurface per unit time

“Electric Current” is theNET amount of chargepassing through a surfaceper unit time

Electric CurrentIn a Conductor, Charges are free to move.

dt

dQI =

The charges may be positive;This is usually relevant only for“special cases” like ions in asolution. (Holes in semiconductorsact like positive charges)

The charges may be negative;This is the normal case formetallic conductors.

Inside a conductor there are LOTS of chargesThere could be 1024 electrons /cm2+

dvr

n = # of charges q per m3

Area A vd is “drift velocity”

AnqvI d=

Current I

Total Current through area A is given by

Current per unit area is given by

dnqvA

IJ ==

J can vary in magnitude and direction in Space

dvnqJrr

= Vector Current Density

Conductors, in general, follow Ohm’s law

For many materials, the local current density is proportional to the local electric field

J

E=! or

ρ is known as the Resistivity of a material

A material with a linear relationship between J and E is said to follow “Ohm’s Law”

!

EJ

vr=

Important note: Not all material follow Ohm’s Law. Most metals do follow Ohm’s Lawso when we speak of a metallic conductor we are implicitly assume that the materialfollows Ohm’s Law. This is not to be confused with a “perfect” conductor which haszero resistivity. There are real materials called “superconductors”

There are many important examples of “Non-Ohmic” materials. Many extremelyimportant semi-conductor devices are non-ohmic.

Current

What is the total Current through this object?

JE

rv!=

L

VE =

IA

LV

AL

VI

AE

I

JAI

!

!

!

=

=

=

=

Ohm’s LawUniform E Field

Collect all the terms that describe the object and

call them “R” the:

RESISTANCEUsual Statement of Ohm’s Law

!

V = IR

Resistivity and Resistance

IMPORTANT:

Do not confuse “Resistivity” withResisitance

Resistivity is a property of a type ofMaterial (copper, steel, water,…)

Resistance is a property of a particular,specific object (a car key, a piece of wire…)

CircuitsDirect Current – “DC”

• In a DC Circuit ALL quantities (Voltage, Current, …) are constant

• Consider that the circuit has been running for a long time and will continue to run longer.

In a steady state system – Charge can only flow in a “Loop”

IE ++

+---

E=0 I=0

V

Current can flow in continuous loopBUT

If Resistance is NOT ZERO,We require something to keep current flowing,

“ELECTRO MOTIVE FORCE” ε

Continuing with “flowing water” analogy: EMF

An Ideal “Electromotive Force” εprovides a constant voltage between two“terminals” –

No Matter How Much Current Flows!

ε

In a closed water “circuit” because ofviscosity (“fluid friction”), there must besome “motive force” to maintain a steadystate flow of water.

In a closed electrical “circuit” because ofresistivity (“electrical friction”), there mustbe some “electro-motive force” to maintaina steady state current.

Inside the “Ideal EMF”

A Non Electrostatic Force acts on the thecharges inside the EMF. This cause the charges tobe displaces and leads to a electrostatic forcewhich “balances” the non-electrostatic force.

nF

r

eF

r

A “resistive” path

Potential difference between ends ofresistive path:

IRV

V

=

= ! } IR=!

Symbols for circuit elements

A

Ideal conductor - generally assume that that R=0

Ideal EMF NOTE – device is asymmetric

Ideal Resistor

EMF with internal resistance

Ideal Voltmeter - generally assume that that R=∞- No current flows through an ideal voltmeter -

Ideal Ammeter - generally assume that that R=0 Electrically, an ideal ammeter is a perfect conductor

Open Circuit EMF Ex 25.2

Question: What do the meters read?

c

No complete circuit means No current

VV

VV

VIRV

VVV

ab

cbab

cbab

cbacab

12

0

==

+=

+=

+=

!

Voltmeter reads V=12 voltAmmeter reads A= 0 amperes

First simplify circuit by replacing the meters by equivalent resistors:

=

Electricallyc

First Determine the Current:

AV

Rr

II

RrIV

IRVtotal

26

12

)(

)(

=!

=+

=

+=

=

Next Determine the Voltage:

VV

AvV

IrV

VVV

ab

ab

ab

accbab

8

)2)(2(12

=

!"=

"=

"=

#

Important Suggestionfor doing problems:

First completely solvethe problemalgebraically…

Then substitutenumerical quantities todetermine thenumerical answer

Open Circuit EMF Ex 25.2

Electric potential through a complete circuit

If I go around the circuit and come back to the same point,

THE VOLTAGE MUST BE THE SAME!

FIGURE 25.20

Power in electric circuitsPower is defined as Energy (Work) per Unit Time

IVdt

dW

dt

dQV

dt

dW

dQVdW

ab

ab

ab

=

=

=

The sign of the power is important

0>dW Power added to system

0<dW Power removed from system

Changes chemical energy toelectrical energy and adds it tothe energy in the circuit

Changes electrical energyto heat and removes itfrom the circuit

For Pure Resistance

R

VRIP

IVdt

dWP

2

2==

== IRV =but

Chapter 25 Summary

Chapter 25 Summary cont.

End of Chapter 25You are responsible for the material covered in T&F Sections 25.1-25.5You are expected to:

• Understand the following terms:Current, Resistivity, Resistance, EMF, Internal Resistance, OpenCircuit, Complete Circuit, Ammeter, Voltmeter, Short Circuit, Power

• Determine Current and Voltage in a simple circuit.

• Understand how voltmeters and ammeter’s are used and how theyrespond.

• Determine power dissipation in a simple circuit

Recommended Y&F Exercises chapter 25:1, 10, 11, 31, 32, 35, 36, 44, 49