Download Resistance and Ohm`s Law

Resistance and Ohm's Law
Resistance and Ohm's Law
●
As the result of successfully completing this unit, the
students will
–
Describe the concept of resistance and
conductance
–
Apply Ohm's Law
–
Determine the power used by a resistor
–
Calculate the resistance and conductance of a
cylindrical resistor
–
Define and identify the special resistance cases:
open circuit and short circuit
Resistance and Ohm's Law
Apply voltage to 2 points of conducting material:
a current will flow.
This current depends on several factors:
- applied voltage
- geometry of material
- electrical properties of material
- temperature
Resistance and Ohm's Law
Apply voltage to 2 points of conducting material:
a current will flow.
This current depends on several factors:
- applied voltage
- geometry of material
- electrical properties of material
- temperature
iv-Characteristic
I
V
Many materials have linear relationship between
voltage and current for a constant temperature.
Resistance and Ohm's Law
V = RI
Ohm's Law
R: resistance
Resistance and Ohm's Law
V =RI
Ohm's Law
R: resistance
Unit of resistance:
(ohm)
[V ] V
[ R]=
= =
[I ] A
Resistance and Ohm's Law
V =RI
Ohm's Law
R: resistance
Unit of resistance:
(ohm)
[V ] V
[ R]=
= =
[I ] A
I
Circuit Element: Resistor
V
R
Conductance
Inverse of resistance: Conductance
1
G=
R
Conductance
Inverse of resistance: Conductance
1
G=
R
Unit of conductance:
(Siemens)
[I] A 1
[G]=
= =Ω=S
[V ] V
Conductance
Inverse of resistance: Conductance
1
G=
R
Unit of conductance:
(Siemens)
Historic Note:
[I] A 1
[G]=
= =Ω=S
[V ] V
[I] A 1
[G]=
= =Ω=
[V ] V
Conductance
Inverse of resistance: Conductance
1
G=
R
Historic Note:
[I] A 1
[G]=
= =Ω=S
[V ] V
[I] A 1
[G]=
= =Ω=
[V ] V
Ω
Unit of conductance:
(Siemens)
Conductance
Inverse of resistance: Conductance
1
G=
R
Historic Note:
[I] A 1
[G]=
= =Ω=S
[V ] V
[I] A 1
[G]=
= =Ω=
[V ] V
Ω
Unit of conductance:
(Siemens)
= mhO
Resistors and Power
Resistors and Power
P =VI
Power dissipated by a resistor
Resistors and Power
2
V
P=VI = I R=
R
2
Power dissipated by a resistor
Cylindrical Resistor
ϱl
l
R= =
A A
R: Resistance
l : Length of Resistor
A: Area of Cross-Section
ϱ : Resistivity
 : Conductivity
A
l
Cylindrical Resistor
ϱl
l
R= =
A A
R: Resistance
l : Length of Resistor
A: Area of Cross-Section
ϱ : Resistivity
 : Conductivity
A
l
Cylindrical Resistor
ϱl
l
R= =
A A
R: Resistance
l : Length of Resistor
A: Area of Cross-Section
ϱ : Resistivity
 : Conductivity
A
l
Resistivity and Conductivity
Material Property:
ϱ
Resistivity:
Conductivity: σ
Resistivity and Conductivity
Material Property:
ϱ
Resistivity:
Conductivity: σ
1
ϱ= σ
Resistivity and Conductivity
Material Property:
ϱ
Resistivity:
Conductivity: σ
1
ϱ= σ
Unit of Resistivity:
[ R ][ A]  m 2
[ϱ ]=
=
= m
[l ]
m
Resistivity and Conductivity
Material Property:
ϱ
Resistivity:
Conductivity: σ
1
ϱ= σ
Unit of Resistivity:
[ R ][ A]  m 2
[ϱ ]=
=
= m
[l ]
m
Unit of Conductivity:
[σ ]=
1
S
=
[ϱ] m
Resistivity and Conductivity
Material Property:
ϱ
Resistivity:
Conductivity: σ
1
ϱ= σ
Unit of Resistivity:
[ R ][ A]  m 2
[ϱ ]=
=
= m
[l ]
m
Unit of Conductivity:
[σ ]=
1
S
=
[ϱ] m
Element
Al
Cu
Au
Fe
Ag
C
ϱ /Ω m
2.73⋅10−8
1.73⋅10−8
2.45⋅10−8
9.98⋅10−8
1.63⋅10−8
3.50⋅10−5
Typical Resistivity values
at Room Temperature
Special Cases
Special Cases
i
v
Open Circuit
R∞
i=0 ∀ v
Special Cases
i
v
i
v
Open Circuit
Short Circuit
R∞
R0
i=0 ∀ v
v=0 ∀ i