# How does length affect the resistance of a wire?

Emma Lazarus

10Y1        10/PLR

Resistance of a wire

## Question

How does length affect the resistance of a wire?

## Prediction

I predict that the longer the wire, the higher the resistance. This is because in a longer wire, there are more wire particles that electrons can bump into. Resistance is caused by electrons colliding with wire particles. If there are more wire particles, the chance of an electron colliding with a wire particle will be higher.

In a longer circuit, it is more of a struggle for electrons to get around the circuit without any collisions. There are many more wire particles (acting like obstacles) to avoid. Electrons cannot increase or decrease speed, but they can collide. They collide with the particles in the wire, therefore less electrons are able to flow than in a shorter length wire. As a result, the ammeter shows a lower current with the same voltage. In a short circuit are less particles of wire. This means less collisions and a lower resistance. I have illustrated this below.

Resistance is caused by collisions – more collisions means more resistance. The reason for these collisions is that in a longer piece of wire, there are more free electrons in the actual atoms of the wire that can carry electricity. When there is an electric field the loose electrons escape towards the positive charge (opposites attract). I have illustrated how the electrons escape the atoms below.

In preliminary work, I wanted to find out which factors affect resistance. In some research I found that there were four factors: temperature, cross-sectional area of the wire, resistivity and the length of the wire. I wanted to find out how exactly each factor affects resistance in a wire. However, before doing this I had to see how resistance varied with potential difference, or I would not know what changes I am going to look out for. I found out that as the potential difference increased, the current increased. P.D. and current were directly proportional to each other.

The formula is potential difference ÷ current, or V/I. It is a constant, and is known as resistance. Length however (among other factors – temperature, cross-sectional area of the wire and resistivity as I stated before) affects resistance in that it increases it as the length itself increases.

Varied resistance occurs due to a condition being changed. For example, in this experiment I will change the length of the wire. By increasing the length of the wire, I am creating more collisions between free wire particles and electrons. This means that more electrons are resisted by the wire, resulting in less current. This has changed one of the things out of V/I (current) and therefore resistance (otherwise known as V/I and usually a constant) will vary. How it will vary is as simple as this: the longer the wire the higher the resistance.

Ohm’s law states that a current flowing through a metal conductor is directly proportional to the voltage across its ends (provided all other conditions are constant). So I know that if we add a variable – in this case length – resistance will change. I expect that the longer the wire, the higher the resistance.

Potential difference is what “pushes” electrons around a circuit. When a wire has more electrons, for the same voltage it produces less current, meaning that there is more resistance. For example, say 6V are being put through a wire, and it produces a current of 3A, we can work out the resistance of this wire by using the formula V/I. 6 ÷ 3 = 2Ω. Now, if we put the same voltage through the same wire, only shorter, it might produce 2A of current. 6 ÷ 2 = 3Ω. So now the resistance would be more, because the current is less. Fewer electrons would be able to flow through the wire, and electron flow is the same as current.

I predict that with a wire length of 0.1m, the resistance will be lowest. I say this because in such a short wire there are not so many particles for passing electrons to collide with. You could compare it to a high street that you are walking down. In the time that you walk down a longer high street you would encounter more obstacles (in the form of people in this case) than you would in a shorter high street (this is assuming the streets are as busy as each other). It is the same with electrons. If they must ...