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Current, Resistance and Electromotive Force Young and Freedman Chapter 25
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
