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Resistance - Ohm's Law

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Introduction

Resistance

Ohm’s Law

As charged particles try to make their way round a circuit they encounter resistance to their flow eg. they collide with atoms in the conductor. More resistance means more energy is needed to push the same number of electrons through part of the circuit.

This resistance is measure in ohms, image00.png.

Definition -“If it takes 1 volt (1 joule per coulomb) to push a current of 1amp through a resistor, it has a resistance of 1 ohm

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.

So imagine an electron travelling through heated copper. It’s trying to avoid collisions with copper atoms. But if the atoms are vibrating, they are going to be easier to hit. More collisions
 more resistance. We say the atoms have a larger collision cross section.

So increasing temperature of a wire leads to increasing resistance.

But, it’s a little more confusing than that because, passing a current through metal causes it to heat up. Why? Collisions between the moving electrons and the metal atoms pass kinetic energy to the atoms, making them shake more. This makes collisions more likely. It’s a vicious circle, isn’t it!!

So most resistors don’t obey Ohm’s Law unless the temperature is kept constant.

Thermistors

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.

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

...read more.

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,

image08.png

image09.png

Here the voltage across all three will be the same but current through each depends on resistance of each.

So:-

image10.png

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.

image11.png

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).

...read more.

Conclusion

Therefore, the 9image02.png 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 9image02.png resistor for a 1image02.png.

image03.png

Find V, the terminal pd, using the same method again:

image04.png

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.

image05.png

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 kimage00.png resistance?

image06.png

image07.png

...read more.

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