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The Internal Resistance of a Battery
The metal contacts which are used to connect a battery into a circuit are called its terminals.  
For this reason, when the voltage of a battery is measured, we often describe the result as the terminal potential difference of the battery.  
 
A battery converts chemical energy into electrical energy.  
The electrical energy given to each Coulomb of charge is called the emf*, E, of the battery.  
Notice from this definition, that emf is a voltage, so in principle can be measured by a voltmeter.  
   
In the following circuits, the voltmeter is assumed to have infinite resistance (a modern digital voltmeter has a resistance of around 107Ω).  
   
If we measure the terminal p.d. of a battery which is not supplying any current (on "open circuit"), the result is equal to the emf of the battery.  
The substances of which the battery is made have some resistance to the flow of electric current.  
This is called the internal resistance of the battery.  
   
Therefore, a more complete way to represent a battery is shown here  
   
(ok, we don't normally draw the dotted outline of the battery... it's just there just to emphasize that r is internal resistance)  
 
We will now consider measuring the terminal p.d. of a battery which is supplying current, as in the next diagram.  
   
   
The energy supplied to each Coulomb of charge by the chemical reactions in the battery is E.  
   
The energy taken from each Coulomb of charge by the internal resistance of the battery is the voltage across the internal resistance, that is, Ir. (This is often called the "lost voltage".)  
   
Therefore, the terminal p.d. of the battery, V, (the reading of the voltmeter) will be given by  
 
which agrees with what was stated above, that the terminal potential difference is only equal to the emf of the battery if the current flowing through the battery is zero.  
   
Notice that the voltmeter in the above circuit is in parallel with the external resistance, R, so V is also given by  
 
so another useful way to express the result is obtained by putting these two equations together, giving  
 
   
* The term "emf" originally came from the phrase electro-motive force. This is now considered an inappropriate term as emf is a quantity of energy not a force. However, the abbreviation is still used.  
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