Transcript NASC 1110

Lecture 5
Current and Resistance
Chapter 17
Outline
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Electric Current
Ohm’s Law
Resistivity
Electrical Energy and Power
Electric Current
An electric current is a flow of like charges (positive
or negative).
The current is the rate at which charge flows through
a conducting surface.
The direction of an electric current is the direction of
positive charge flow (current carriers are electrons).
Q
I
t
Unit of current is ampere (A)
1A  1C/s
1A of current is equivalent to 1C of
charge passing through the crossectional
area in a time interval of 1 second.
Electric Current
Microscopic view of electric current
Representation of electric current
Resistance
When a potential difference (V) is applied across
the end of a conductor, the current in the
conductor is proportional to the applied voltage.
I ~ V
The proportionality constant R is called the resistance.
It remains constant over a wide range of currents and
voltages.
V
R
I
Ohm’s Law
The relationship between the current and voltage is
called Ohm’s Law after George Ohm.
V = IR
Unit of resistance is ohm ()
V is the potential drop across the resistor
I is the current in the resistor
Materials with a constant resistance are called ohmic,
those with variable resistance are nonohmic.
Using Ohm’s Law
Problem: How long can a car with a 12V battery
of 60 A h capacity have the lights, of total
resistance of 4 , on before the battery runs down?
Solution: I = V /R = 12V / 4  = 3 A
Time t = 60 A h / 3 A = 20 hours
Resistivity
Electrons, driven by the electric force inside a
conductor, collide with atoms and experience an
internal friction.
This is the origin of a material’s resistance.
The resistance of an ohmic conductor is directly
proportional to its length (l) and inversely
proportional to its cross-sectional area (A).
l
R=
A
The constant  is called the resistivity
of the material.
=R A / l   is measured in  m
(ohm-meters).
Resistance of a Wire
Problem: Calculate the resistance per unit length
of an aluminum (Al) wire of radius 0.5 mm.
Solution: The cross-sectional area is A =  r2
A = 3.1416 (0.5 103 m)2 = 7.85 107 m2
The resistivity of Al is 2.82 10 8  m
Resistance per unit length is R/l = /A

2.82 10 8  m
 =  = 0.036 /m
A
7.85 107 m2
Electrical Energy and Power
The chemical energy of a battery is constantly
transformed into internal energy of a conductor.
Q
 V = I V
t
Power P = I V
V = I R  P=I2R= (V)2/R
Unit of power
1W = 1V 1A
Units of Power and Energy
Unit of power is Watt (W).
Power is energy per unit time.
Thus, energy can be measured in kilowatt-hours.
This is not a standard unit, because the SI unit for
power is W and for time is s.
1 kWh = (103 W) (3600 s) = 3.6 106 J
Summary
• Electric current is a flow of charge in an electric
field
• Resistance of a conductor is the ratio of the
potential difference across the conductor to the
current
• Ohm’s law states that the potential difference is
directly proportional to the current
• Resistivity is an intrinsic property of a
conductor characterizing its ability to resist to
the current