General Physics II
By
Dr. Cherdsak Bootjomchai
(Dr.Per)
Chapter 5
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.
106 m/s electron
motion velocity
10-4m/s Drift velocity
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
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.
dQ
I=
dt
(25-1)
1 mA (milliampere) = 1 x 10-3 A (ampere)
1 µA(microampere) = 1 x 10-6 A (ampere)
Conventional Current Direction
Chapter 25
5
Electric Current Density
Current, Drift Velocity, and Current Density
dQ = q ( nAv d dt ) = nqv d Adt
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
I
J =
= current density in amperes/m2
A
Chapter 25
6
Resistivity
r
r
vd = µE
Drift Velocity
where µ = mobility of conducting material
Drift Velocity is 1010 slower than Random Velocity
E
ρ=
J
Definition of resistivity in ohm-meters (Ω
Ω-m).
where
r
r
r
r
J = nq v d = nq µ E = σ E
σ = nqµ
conductivity of the material.
1
1
E
ρ= =
=
σ nqµ J
Chapter 25
7
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
r
r 1 r
J = σE = E
ρ
J=
1
ρ
E
J =
I
A
E=
V
L
for a uniform E
–
+
V =
1V
I
=
A ρ L
I
L
ρ L = ( ρ ) I = RI
A
A
Figure 25-7
therefore
V = RI
Ohm’s Law
where R is the resistance of the material in ohms (Ω
Ω)
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
1
I= V
R
Nonlinear
1
Slope =
R
Nonlinear
Ohm’s law applies
V = RI
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
–
EMF
Ideal source of
electrical energy
–
VR = EMF = R I
rs
+
EMF
–
Real source of
electrical energy
I=
I
Real Source
Internal source
resistance
Voltage drop in
current direction
R
a
+
Vab
VR EMF
=
R
R
External resistance
R
Vab = EMF − Irs = IR
–
b
16
A Source with an Open Circuit
Ex. The figure shows a source (a battery) with an emf (ε) of 12 V and an
internal resistance r of 2 Ω. Determine the reading of the idealized voltmeter
V and the idealized ammeter A.
I = 0 amps
Vab = EMF − Ir = 12V − 0 r = 12V
Chapter 25
17
A source in a complete circuit
Ex. From the figure, what are the voltmeter and ammeter readings
Vab = ε − Ir = IR
ε = IR + Ir = I ( R + r )
I=
ε
R+r
=
12
= 2A
4+2
Vab = ε − Ir = 12 − 2( 2) = 8V
Vab = Va 'b ' = IR = 2( 4) = 8V
18
A Source with a Short Circuit
Ex. From the figure, what are the meter readings now ?
V ab = 0
I=6A
V ab = ε − Ir = IR = I ( 0 ) = 0
ε − Ir = 0
ε = Ir
Chapter 25
I =
ε
r
=
12V
= 6A
2Ω
19
Potential Rises and Drops in a Circuit
20
Energy and Power
I =
dQ
dt
dWab
Vab =
dQ
dWab = Vab Idt
1 watt = 1 joule/sec
dW ab
P=
= Vab I
dt
dQ = Idt
dWab = Vab dQ
watts
Pure Resistance
21
Power Output of an EMF Source
I
rs
+
+
a
– +
Vab
EMF
–
R
–
b
Vab = EMF − Irs = IR
Pab = Vab I = ( EMF − Irs ) I = ( EMF) I − I 2 rs = I 2 R
( EMF ) I = I 2 rs + I 2 R
Power output of battery
Power dissipated in R
Power dissipated in battery resistance
Power supplied by the battery
22
Power Input to a Source
I
rs
+
–
a
+
Vab greater then the EMF of the battery
+
EMF
Vab
–
–
b
Vab = EMF + Irs
Pab = Vab I = ( EMF + Irs ) I = ( EMF) I + I 2 rs
Vab I = ( EMF ) I + I 2 rs
Power dissipated in battery resistance
Power charging the battery
Total Power input to battery
23
Power Input and Output in a Complete Circuit
Ex. From the figure, fine the rate of energy conversion (chemical to electrical)
and the rate of dissipation of energy (conversion to heat) in the battery and the
net power output of the battery.
24
Power in a Short Circuit
Ex. From the figure, fine the rates of energy conversion and energy
dissipation in the battery and the net power output of the battery
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.
26
A microscopic look at conduction
The end of Chapter 5
Current, Resistance and
Electromotive Force