The resistance of a conductor is a
measure of the opposition it offers to the flow of electric
current. 



The resistance of a component causes electrical energy to be
converted into thermal energy. 



The resistance of a component is the potential difference per
unit current. In other words, the voltage needed to cause one
Amp of current to flow through the component. 

Writing this definition as an equation we
have 





The units of current are therefore
VA^{1} but a resistance
of 1VA^{1} is called
1Ohm (1Ω)
after Georg Simon Ohm 



Ohm investigated the resistance of metals. He wanted to find how
the resistance of a piece of metal depends on its dimensions. 

He found that the resistance of a piece of metal is directly
proportional to its length, L and inversely proportional
to its cross sectional area, A. 



Therefore, we can write 



Not surprisingly, he also found that resistance depends on the
type of metal being investigated. 

The constant of proportionality, ρ
is a number which depends on the type of metal. 

It is called the resistivity of the metal. 



and by looking at this equation we can state that the units of
resistivity must be Ωm 



Ohm's Law 

Ohm also investigated the relation between the voltage across a
given piece of metal and the current flowing through it. His results
gave what is now called Ohm’s law, which is stated as follows: 

For a metal conductor at
constant temperature, the current flowing through it is
directly proportional to the voltage across it. 

As voltage divided by current is resistance, this law tells us
that the resistance of a piece of metal (at constant temperature) is
constant. That is, the resistance of a piece of metal is
independent of the applied voltage.


This is not always true, for example, the graph below
shows how the current varies with applied voltage for a filament
light bulb. 




Clearly the current is not proportional to the
voltage in this case.
This is because the filament
temperature increases as the current flowing through it
increases.
The way the graph curves tells us that the
resistance of the filament (a small piece of metal)
increases as the temperature increases.
This is
true for all metals but not for all other
conductors. 

