Resistance  Ohm's Law
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Introduction
Resistance 

This equation summarises Ohm’s law. It suggests that any value of voltage you put across a resistor divided by the current it produces in the resistor, will always give the same value of resistance. So, if you plotted a graph you would get:
The effect of temperature on resistance  
If an atom is heated it gains Ek. If it’s in a solid conductor eg. copper, that means it vibrates on the spot more.  
 
Some devices break the rule we’ve just explained (typical) and reduce their resistance as temperature increases. This is because the extra energy makes the atoms release electrons, allowing them to move more easily.  
Combinations of resistors  
If you have more than one resistor in a circuit it is often useful to be able to calculate a value of a single resistor which would be the same as the actual combination of resistors 
Middle
Current used in all 3 will be the same (current doesn’t get used up) but energy used per coulomb (i.e. pd) will depend on value of resistance
So,
Here the voltage across all three will be the same but current through each depends on resistance of each.
So:
Internal resistance  
Batteries are not perfect (what is  apart from the moment your last exam finishes, of course?!). Use them for a while and you notice they get hot. Where is the heat energy from? It’s from the stored (potential) energy in every battery. So batteries turn some of their available energy into heat inside themselves. It is easy to explain if you imagine that each cell is perfect except that for some bizarre reason (probably part of a plot to take over the world, masterminded by Dr Evil) the manufacturers put a resistor in series with it inside the casing. 
Therefore, inside the cell you get some energy put IN to the circuit by the cell (an emf) some energy taken OUT of the circuit by the resistor (a pd).
Conclusion
Therefore, the 9 resistor gets V = IR = 0.2 x 9 = 1.8V
So this 2V emf cell actually supplies 1.8V to the external circuit.
Now, swap the 9 resistor for a 1.
Find V, the terminal pd, using the same method again:
So the 2V emf cell actually supplies 1V!!! The other 1 V is used making the cell hot. Not very efficient. You need to consider the internal resistance when deciding if a cell is appropriate to use with a particular circuit. The external resistance must be much greater than internal resistance.  
Voltmeters have resistance  
We always assume ammeters and voltmeters are perfect. 
The perfect ammeter must have zero resistance.
The perfect voltmeter must have infinite resistance.
Otherwise, when you put them into the circuit they would change the circuit.
In reality they aren’t perfect. So in the circuit above, some of the emf supplied to the circuit is used pushing current through the ammeter, and some of the current goes through the voltmeter, not through R.
How can you deal with this? Well, pretend that the voltmeter is actually not a voltmeter but just a resistor and look at the effect it has.
Example:
What should the current, I, be in this circuit if the voltmeter is
(a) perfect (infinite resistance)
(b) 20 k resistance?
This student written piece of work is one of many that can be found in our GCSE Electricity and Magnetism section.
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