The resistance of a conductor depends on its length, cross-sectional area, and material composition. Resistance increases with length, decreases with area, and varies between materials. Ohm's law states that current is directly proportional to voltage and inversely proportional to resistance. Power dissipated in a resistance is calculated using P=IV, P=I^2R, or P=V^2/R, and causes the resistance to increase in temperature.

1. Resistance
The resistance of a conductor is,
a. directly proportional to its length.
(resistance increases with conductor length)
b. inversely proportional to its cross-sectional area.
(resistance decreases with conductor area)
c. dependent on the material composition.
(different materials resist the flow of electrons to a lesser or greater extent,
this is called resistivity)
Resistance can vary slightly with temperature, for all our
calculations we will assume a constant temperature.

2. Resistivity
The resistivity (rho, ρ) of a conductor is dependent upon the
‘willingness’ of the material to allow the flow of electrons.
Resistivity has a positive temperature coefficient, meaning that an
increase in temperature increases the resistivity of the material.
Material ρ Ω/m at 20°C
Silver 1.64 x 10-8
Copper 1.76 x 10-8
Aluminium 2.8 x 10-8
Brass 7.2 x 10-8
Eureka 49 x 10-8
Glass 10 x 1012
Mica 9 x 1013
Resistivity of some common materials at 20°C
Conductors
Insulators
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3. Resistance of a Conductor
The resistance (R) of a material is dependent upon the physical dimensions,
the material temperature and its resistivity.
Knowing these parameters it is possible to determine the resistance of a given
sample.
The unit of resistance is the Ohm (omega, Ω).
where l is the length of the conductor
a is its cross sectional area in m2
ρ is the resistivity of the material.
Activity
Determine the resistance of three different conducting materials with the
following dimensions, l = 1km, a = 2.0mm2
.
If the cross sectional area were to double what would you expect to happen
to the resistance.
If the temperature was to rise what would be the effect on the resistance.
R = ρ l ohms
a

4. Resistance and Ohms Law
The German physicist Georg Simon Ohm (1789 – 1854) developed a
law which defined the relationship between electric current, voltage
and resistance from a series of experiments, representing the
beginning of electric circuit analysis.
Ohm’s Law
The current flowing in a circuit is directly proportional to the applied
emf and inversely proportional to the resistance of the circuit.
I =
V amps
R
R =
V ohms
I
V =IR volts

5. Resistance and Ohms Law
Activity
1. A 15 ohm resistance is connected to a 30 volt battery, determine
the current flowing through the circuit.
2. An ammeter shows that a current of 4 amps is flowing in a circuit. If
the supply voltmeter shows that the supply is set to 100 volts
determine the circuit resistance.
3. Determine the voltage required to pass a current of 5 amps through
a 100 ohm resistance.
It is a good idea to sketch these circuits before starting to calculate
the results.

6. Power Dissipated in Resistance
When an electric current passes through a resistance electrons collide
with fixed atoms causing energy to transfer from electron to atom and
thus work is done.
The rate at which work is done is called power, this work causes the
resistance to increase in temperature.
The unit of power is the Watt, symbol “W”.
The power dissipated in a resistance can be determined using any of
the three methods below;
P =
V2
watts
R
P =VI watts
P =I2
R watts

7. Power Dissipated in Resistance
Activity
1. Determine the power dissipated in a 15 ohm resistance connected
to a 30 volt supply.
2. An ammeter shows that a current of 4 amps is flowing in a circuit. If
the supply voltmeter shows that the supply is set to 100 volts
determine the power taken from the supply.
3. A current of 3 amps flows through a 10 ohm resistance, determine
the power dissipated in the resistance. If the resistance has a
temperature coefficient of 0.5°C/watt and the ambient temperature
is 20°C determine the final temperature reached.
It is a good idea to sketch these circuits before starting to calculate
your results.