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Resistance
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 Ω  
   
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 Ohmís 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.
 
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