Lecture 5 Current and Resistance

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Lecture 5Current and Resistance
Chapter 17
Outline

• Electric Current
• Ohms Law
• Resistivity
• Electrical Energy and Power

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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).
Unit of current is ampere (A) 1A ? 1C/s
?Q I ? ? ?t
1A of current is equivalent to 1C of charge
passing through the crossectional area in a time
interval of 1 second.
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Electric Current
Microscopic view of electric current
Representation of electric current
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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
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Ohms Law
The relationship between the current and voltage
is called Ohms 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.
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Using Ohms 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
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Resistivity
Electrons, driven by the electric force inside a
conductor, collide with atoms and experience an
internal friction. This is the origin of a
materials resistance. The resistance of an ohmic
conductor is directly proportional to its length
(l) and inversely proportional to its
cross-sectional area (A).
The constant ? is called the resistivity of the
material. ?R A / l ? ? is measured in ? m
(ohm-meters).
l R ? ? A
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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
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Electrical Energy and Power
The chemical energy of a battery is constantly
transformed into internal energy of a conductor.
?Q ?? ?V I ?V ?t
Unit of power 1W 1V 1A
Power P I ?V ?V I R ? PI2R (?V)2/R
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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
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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
• Ohms 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