Resistance and wire length

Physics · Resistance

Every piece here is the same wire: same metal, same thickness. The only thing you change is the length. Resistance is shown compared with the 1-length piece.

Predict, then check

The potential difference (p.d.) across the wire stays exactly the same the whole time.

A wire is connected across a fixed p.d. You swap it for a piece of the same wire that is three times as long. What happens to the current?

Finding resistance from two measurements

Resistance = potential difference ÷ current. Tap resistance to cover it, then see how the other two give it. The numbers are an example: 6 V across a wire with 0.5 A through it.

Tap the quantity you want to find. The triangle shows you the formula.

Investigating length and resistance

Step through the method in order.

1. 1Keep the wire the sameUse one kind of wire the whole way through: the same metal and the same thickness, kept at the same temperature.+
2. 2Change the lengthTest one length of the wire, then try other lengths, shorter and longer.+
3. 3Measure two thingsAt each length, measure the current through the wire and the potential difference across it.
4. 4Calculate the resistanceFor each length, work out resistance = p.d. ÷ current, in ohms.
5. 5Plot the graphPlot resistance against length. Ideally the points lie on a straight line through the origin.+

What you need to know

• Resistance is how much something opposes the flow of charge (the current). It's measured in ohms (Ω).
• Resistance = potential difference ÷ current (volts ÷ amperes gives ohms).
• For the same material and thickness, a longer wire has a bigger resistance, and a shorter wire has a smaller one.
• With a fixed p.d., more resistance means less current.

The big picture

For a wire of the same material and thickness, resistance is proportional to length: double the length and the resistance doubles. That's because the charges have further to travel through the metal, meeting more opposition on the way. With a fixed p.d., a longer wire therefore lets less current through. You find resistance from measurements as p.d. ÷ current, in ohms.

⚠ Watch out

Thinking a longer wire 'carries more' and so lets more current through. It's the other way round: for the same material and thickness, more length means more resistance, and with the same p.d. that means less current.

Memory hook

Crowded corridor: make it twice as long and there are twice as many people to squeeze past. Twice the wire, twice the resistance — and with the same push (p.d.), less current gets through.

Check yourself

In three linked steps, explain why a longer piece of the same wire lets less current through at the same p.d. Then settle the opening puzzle: what happens to the resistance of each half?