Download Lecture Notes: Y&F Chapter 25

Electric Current An Analogy – Water Flow in a Pipe
H20
gallons/minute
Individual molecules are
bouncing around with
speeds of km/s!
“Flow Rate” is the NET amount
of water passing through a
surface per unit time
Net water velocity is m/s
I
Coulombs/s
“Electric Current” is the
NET amount of charge
passing through a surface
per unit time
- - - - - -
Individual electrons are
bouncing around with
very high speed
Electron “drift velocity
may be mm/s
Electric Current
In a Conductor, Charges are free to move.
The charges may be positive;
This is usually relevant only for
“special cases” like ions in a
solution.
The charges may be negative;
This is the normal case for
metallic conductors.
The Direction of the Electric “Current” is given by the “flow” of positive charge
dQ
I=
dt
Inside a Conductor there are LOTS of charges
(There may be ~1024 electrons per cm3)
Area A
Current I
vd is “drift velocity”
r
vd
n = # of charges q per m3
Total Current through area A is given by
I = nqvd A
Current per unit area is given by
I
J = = nqvd
A
J can vary in magnitude and direction in Space
r
r
J = nqvd
Vector Current Density
For many materials, the local current density is
proportional to the local electric field
E
ρ=
J
or
r
J=
v
E
ρ
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”
Important note: Not all material follow Ohm’s Law. Most metals do follow Ohm’s Law
so when we speak of a metallic conductor we are implicitly assume that the material
follows Ohm’s Law. This is not to be confused with a “perfect” conductor which has
zero resistivity. There are real materials called “superconductors”
There are many important examples of “Non-Ohmic” materials. Many extremely
important semi-conductor devices are non-ohmic.
V
E=
L
r
v
E = ρJ
Ohm’s Law
Uniform E Field
What is the total Current through this object?
I = JA
I=
E
ρ
A
V
A
Lρ
Lρ
V=
I
A
I=
Collect all the terms that
describe the object and
call them “R” the:
RESISTANCE
V = IR
Usual Statement
of Ohm’s Law
IMPORTANT:
Do not confuse “Resistivity” with
Resisitance
Resistivity is a property of a type of
Material (copper, steel, water,…)
Resistance is a property of a particular,
specific object (a car key, a piece of wire…)
Circuits
Direct 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”
E
I
-
+
+
+
E=0 I=0
V
Current can flow in continuous loop
BUT
If Resistance is NOT ZERO,
We require something to keep current flowing,
“ELECTRO MOTIVE FORCE”
ε
Continue our analogy with flowing water
In a closed water “circuit” because of viscosity
(“fluid friction”), there must be some “motive
force” to maintain a steady state flow of water.
In a closed electrical “circuit” because of
resistivity (“electrical friction”), there must be
some “electro-motive force” to maintain a steady
state current.
ε
An Ideal “Electromotive Force” ε provides a
constant voltage between two “terminals” –
No Matter How Much Current Flows!
Inside the “Ideal EMF”
r
A Non Electrostatic Force Fnacts on the the charges
inside the EMF. This cause the charges to ber
displaces and leads to a electrostatic force Fe which
“balances” the non-electrostatic force.
A “resistive” path
Potential difference between ends of
resistive path:
V =ε
V = IR }
ε = IR
Symbols for Circuit elements
Ideal conductor - generally assume that that R=0
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 -
A
Ideal Ammeter - generally assume that that R=0
Electrically, an ideal ammeter is a perfect conductor
Open Circuit EMF – Y&F Conceptual Example 25.2
Question: What do the meters read?
First simplify circuit by replacing the meters by equivalent resistors:
No complete circuit means No current
c
Vab = Vac + Vcb
Vab = IR + Vcb
Vab = 0 + Vcb
Vab = ε = 12V
Voltmeter reads V=12 volt
Ammeter reads A= 0 amperes
Open Circuit EMF – Y&F Conceptual Example 25.2
=
c
Electrically
First Determine the Current:
V = IRtotal
V = I (r + R)
I
12V
I=
=
= 2A
( r + R ) 6Ω
Next Determine the Votage:
Vab = Vcb − Vac
Vab = ε − Ir
Vab = 12v − ( 2 A)( 2Ω)
Vab = 8V
Important Suggestion
for doing problems:
First completely solve
the problem
algebraically…
Then substitute
numerical quantities to
determine the numerical
answer
Electrostatic Potential through a complete circuit
FIGURE 25.20
If I go around the circuit and come back to the same point,
THE VOLTAGE MUST BE THE SAME!
Power in Electric Circuits
Power is defined as Energy (Work) per Unit Time
dW = VabdQ
dQ
dW
= Vab
dt
dt
dW
= Vab I
dt
For Pure Resistance
dW
P=
= IV
dt
V2
2
P=I R=
R
but V = IR
The sign of the power is important
dW > 0
Power added to system
Changes chemical energy to
electrical energy and adds it
to the energy in the circuit
dW < 0
Power removed from system
Changes electrical energy to
heat and removes it from the
circuit
End of Chapter 25
You are responsible for the material covered in T&F Sections 25.1-25.5
You are expected to:
•
Understand the following terms:
Current, Resistivity, Resistance, EMF, Internal Resistance, Open Circuit,
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 they respond.
•
Determine power dissipation in a simple circuit
Recommended F&Y Exercises chapter 25:
•
1,13,31,35,37,43,49