The length of a metal wire is doubled. What happens to its resistance?

It doubles. R is proportional to L.

The diameter of a wire is doubled and its length is unchanged. What happens to its resistance?

It falls to a quarter. The area is four times bigger.

What does the resistivity of a wire depend on?

the material it is made of. Length and area change the resistance, not the resistivity.

Resistivity · Cambridge A Level Physics 9702 revision

In plain words

Part of a wire's resistance is down to its shape: long and thin is harder to get through than short and fat. The rest is down to what it is made of, and that part is called resistivity. Copper's is tiny, which is why cables are made of it.

Three things to know

R = ρL ÷ A, so ρ = RA ÷ L. Resistivity ρ is a property of the material, measured in Ω m.
Resistance is proportional to length, and inversely proportional to cross-sectional area.
To measure ρ: measure the diameter of a wire with a micrometer (for A = πd² ÷ 4), then find its resistance for several lengths. A graph of R against L is a straight line through the origin with gradient ρ ÷ A.

Worked example

Find the resistance of a copper wire 2.0 m long with a cross-sectional area of 5.0 × 10⁻⁷ m². (Resistivity of copper = 1.7 × 10⁻⁸ Ω m.)

R = ρL ÷ A.
= 1.7 × 10⁻⁸ × 2.0 ÷ 5.0 × 10⁻⁷.
= 0.068 Ω.

Tips and tricks

Double the length and the resistance doubles. Double the diameter and the resistance falls to a quarter, because the area is four times bigger.
In the experiment keep the current small, so the wire doesn't warm up and change its resistance.

5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Resistivity: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

What are the units of resistivity?
- Ω
- Ω/m
- Ω m (the answer)
- Ω m²
From ρ = RA ÷ L.
The length of a metal wire is doubled. What happens to its resistance?
- It halves.
- It stays the same.
- It doubles. (the answer)
- It becomes four times bigger.
R is proportional to L.
The diameter of a wire is doubled and its length is unchanged. What happens to its resistance?
- It doubles.
- It halves.
- It falls to a quarter. (the answer)
- It becomes four times bigger.
The area is four times bigger.
What does the resistivity of a wire depend on?
- the material it is made of (the answer)
- its length
- its cross-sectional area
- the current in it
Length and area change the resistance, not the resistivity.
On a graph of resistance against length for a uniform wire, what is the gradient?
- ρ ÷ A (the answer)
- ρ
- ρA
- A ÷ ρ
R = (ρ ÷ A) × L.

5 questions

Tap an answer and you’ll see straight away whether it’s right, and why.

Worksheet

3 questions, 7 marks. Write your answers on paper, then check them.

Resistivity

Cambridge International AS & A Level Physics 9702 · 7 marks · papermunch.org

Name ______________________________ Date ______________

A wire has a resistance of 4.0 Ω. Find the resistance of a wire of the same material that is twice as long and has twice the cross-sectional area.[2]
Show answerHide answer
4.0 Ω. The two changes cancel.
I got this one
A wire 1.5 m long with a cross-sectional area of 2.0 × 10⁻⁷ m² has a resistance of 8.25 Ω. Find the resistivity of its material.[3]
Show answerHide answer
1.1 × 10⁻⁶ Ω m. 8.25 × 2.0 × 10⁻⁷ ÷ 1.5.
I got this one
A wire has a diameter of 0.40 mm. Find its cross-sectional area in m².[2]
Show answerHide answer
1.3 × 10⁻⁷ m². π × (0.20 × 10⁻³)².
I got this one

Answers: Resistivity

1. 4.0 Ω. The two changes cancel.
2. 1.1 × 10⁻⁶ Ω m. 8.25 × 2.0 × 10⁻⁷ ÷ 1.5.
3. 1.3 × 10⁻⁷ m². π × (0.20 × 10⁻³)².