A basic guide to resistance.

Electron Flow Model

Everything is made of very small particles called atoms.

Each atom has a heavy positively charged nucleus and is surrounded by a cloud of light, negatively charged, electrons.

In metals, the outer most electron of each atom is weakly attracted to the positive nucleus and can escape from the atom and wander around between the atoms. Note 1

So, in metals, we have all these millions and millions of electrons whizzing about at high speed, in random directions, between the fixed atoms.

When you connect the piece of metal across a battery all these electrons are still whizzing about at random, BUT they are also forced to slowly drift in one direction. This slow drift is called the current.

Note 2

As the electrons are forced through the metal they collide with the atoms and transfer energy to them. This is where the word resistance comes in. The electrons experience resistance to their forced movement between the atoms.

When the electrons collide with the atoms the electrons lose energy and slow down, the atoms gain energy and vibrate faster. You should know that the faster the vibration of particles the hotter the temperature of the material is.

So the energy from the battery, that is used to force the electrons to move, is transferred to the atoms, and we see this as the metal getting hotter. The resistance of a metal always leads to a heating effect when a current is passed through it. The size of the resistance will depend on the type of metal, and its dimensions.

Note 1

The regular arrangement of atoms in metals is called the “lattice” or “crystal lattice”. The electrons are not completely free from the nuclei so it is not quite correct to describe the electrons as “free electrons” or the atoms as “positive ions”. However, in many books you will see metals described as “a sea of electrons moving randomly through a lattice of positive ions.” In newer books and your GCSE specification you might find the atom parts described as “positive atomic kernels”. Anyway, this whole arrangement is known as “metal bonding” and the attraction of the electrons to the positive atomic kernels produces the characteristic properties of metals.

Note 2

The current in a metal is due to the drift of electrons. Without the atomic model many people get the idea that charges (electrons) flow out of one end of a battery, through the wire, and then back in to the other end of the battery. With the atomic model you see that this is not really correct. The metal is full of “free” electrons, and when you connect a battery they all start to slowly drift through the wire, and of course through the material of the battery itself. Note that the drift of the electrons is very slow. It may take them half an hour to move through a metre length of wire. The continuous random motion of the electrons is very fast in comparison, typically a thousand metres per second.

Note 3

A more advanced model would be based upon Quantum Theory. This is beyond the scope of the GCSE specifications.

Last edited by Webmaster on Tue Mar 23, 2004 3:34 pm; edited 1 time in total

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Resistance/length of wire – Atomic model

Resistance increases with length.

As you increase the length you increase (proportionally) the number of atoms and hence the number of moving electrons when a current flows.

If you, say, double the length of wire, you double the number of moving electrons, and so double the number of collisions.

Suppose we double the length of wire and then adjust the voltage across the wire so that the current remains the same as it was before. As the current is the same the average energy lost by a single electron during an average collision is the same as before. BUT the total energy lost is now twice as much, because there are twice as many moving electrons and twice as many collisions.

The voltage across the wire is defined as the energy transferred per unit charge. i.e. the energy transferred in pushing one coulomb of charge through the wire. If we imagine pushing one coulomb of electrons from one end of the wire to the other, then we have just worked out that there will be twice as many collisions and twice as much energy transferred. So, by definition, the voltage across the wire must also have doubled.

Resistance = voltage / current

R1 = V/I for the original length

R2 = 2V/I = 2R1 for the double length

i.e. double the length, double the resistance.

CONCLUSION

Resistance is directly proportional to the length of the wire.

Remember that 1 coulomb is just a big number of electrons (about 6 million million million). If you had a current of 1 amp and could look at a single point in the wire then this many electrons would flow past you each second. It is easier to think of pushing just one electron from one end of the wire to the other. It is easy to see that the electron will have twice as many collisions. The voltage really tells you how much energy each electron loses as it is pushed from one end of the circuit to another. So the size of the current (i.e. the number of electrons flowing) and the size of the voltage (i.e. amount of energy transferred per electron) both contribute to the total amount of energy transferred.

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Resistance/Thickness of wire

We can use the same theory for wires of different thickness. In this case it is better to think in terms of the cross-sectional area of the wire, rather than the diameter. This is because if you double the cross-sectional area, keeping the length the same, then you double the number of atoms and double the number of free electrons.

Ok, so using the same theory as before we use a second wire with twice the cross-sectional area of the first wire and the same length. If we keep the electrons flowing at the same average speed as in the first wire, then because there are now twice as many electrons flowing the current will be twice as big.

The amount of energy transferred by an individual electron as it flows from one end of the wire to the other is the same because it travels the same distance and has the same number of collisions. This means the energy transferred per coulomb of charge is the same. The voltage is defined as the energy transferred per coulomb of charge so the voltage between the two ends of the wire is still the same*.

The energy transferred per electron is the same, but the number of electrons flowing has doubled, so the total energy transferred has also doubled.

R1 = V/I for the original cross-sectional area.

R2 = V/2I = R1/2 for twice the area.

i.e double the cross-sectional area, half the resistance.

CONCLUSION

Resistance is inversely proportional to the cross-sectional area of the wire

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Don’t forget to do some good diagrams to help explain this. Show two wires, one with double the number of atoms and free electrons as the other

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And don’t forget how to calculate the area of a circle:

Area = pi x radius squared

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* This may seem odd but if you think about it this is how batteries or power supplies work. It is one of the basic rules of circuits that is often not explained – Power supplies and batteries will always try and keep the same output voltage, regardless of what you connect to them. So if you connect something with a low resistance a big current flows, and if you connect something with a high resistance a small current flows.

Another way to look at this problem is to imagine that the wire with twice the area is split along its length. It is then like two of the original wires in parallel. You can then use the rule or formula for resistors in parallel to show that the current doubles and the voltage stays the same.