Resistivity — the “personality” of a material in a circuit (with simple practicals)

If you’ve ever swapped one bit of wire for another and thought, “Hang on… why has the current changed when the battery hasn’t?” — congratulations, you’ve stumbled into resistivity.

Resistance vs resistivity (the bit everyone muddles up)

• Resistance (R) is the opposition to current of a particular component (this bit of wire, this resistor, this filament). It depends on shape as well as material.

• Resistivity (ρ) is a property of the material itself. Think of it as how stubborn the material is about letting charge move through it.

The link between them is:

$$R = \rho \frac{L}{A}$$

Where:

• $R$ = resistance (Ω)

• $ρ$ = resistivity (Ω m)

• $L$ = length (m)

• $A$ = cross-sectional area (m²)

So if you keep the material the same:

• Longer wire → bigger $L$ → bigger R

• Thicker wire → bigger $A$ → smaller R

That’s why the chunky cables on a car battery look like they mean business: they do.

What resistivity really means (in plain words)

In metals, electrons are the charge carriers. A low resistivity material (like copper) lets electrons drift through fairly easily. A high resistivity material (like nichrome) makes life harder for them, so you get more resistance for the same size wire.

And when the resistance is bigger, for a given voltage:

• the current drops

• and the heating effect can increase in the resistor/wire (handy for toasters… less handy for your extension lead).

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Practical 1: Length of wire vs resistance (the “slide contact” classic)

Aim: show $R \propto L$ for a uniform wire.

You need

• a length of constantan or nichrome wire stretched straight along a metre rule

• low-voltage DC supply (1–3 V is plenty)

• ammeter, voltmeter, crocodile clips (or a sliding contact), leads

Method

1. Connect the wire in series with the ammeter and supply.

2. Put the voltmeter across the measured length of wire (e.g. 20 cm, 40 cm, 60 cm…).

3. For each length, record V and I.

4. Calculate $R = V/I$ for each length.

5. Plot R (y-axis) against L (x-axis).

Expected result

• You should get a straight line through (or very near) the origin.

• The gradient equals $ρ/A$. (Which feels very satisfying if you like that sort of thing.)

Good practice / reliability tips

• Use low current so the wire doesn’t heat up (temperature changes resistance).

• Take readings quickly, or allow cooling time between measurements.

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Practical 2: Thickness of wire vs resistance (same material, different diameters)

Aim: show $R \propto 1/A$.

You need

• two or three wires of the same material and length but different diameters (e.g. copper or constantan)

• micrometer (or vernier caliper) to measure diameter

• same circuit as above

Method

1. Keep length the same each time.

2. Measure diameter $d$, calculate area $A = \pi(d/2)^2$.

3. Measure V and I, calculate R.

4. Compare R values (or plot R against $1/A$).

Expected result

• Thicker wire (bigger A) gives smaller R.

• A plot of R vs 1/A should be roughly linear.

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Practical 3: Same length, different materials (why nichrome is used in heaters)

Aim: compare resistivity between materials.

You need

• equal lengths of copper, steel, nichrome/constantan (where possible)

• same measurement setup

Method

1. Keep L as close as possible to the same for each sample.

2. Measure V and I → find R.

3. If you can estimate A, you can go further and calculate:

   $$\rho = R\frac{A}{L}$$

Expected result

• Copper tends to show low resistance.

• Nichrome/constantan higher resistance — ideal where you want resistance without needing miles of wire.

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Temperature: the twist in the plot

Resistivity isn’t just “a number in a table” — it changes with temperature.

• Metals: resistivity usually increases with temperature (more lattice vibrations → more collisions).

• Semiconductors (like thermistors): resistivity usually decreases with temperature (more charge carriers become available).

A quick demo: put a small filament lamp in circuit and increase the voltage. The filament heats up and its resistance rises — that’s why the I–V graph curves.

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Common student mistakes (and how to avoid them)

• Mixing up R and ρ: resistance is for an object, resistivity is for a material.

• Forgetting units: resistivity is Ω m, not Ω.

• Letting the wire heat up: you’ll measure temperature effects instead of the length/area effect.

• Measuring length but not keeping contact points consistent: crocodile clips can be sneaky.

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A neat conclusion

Resistivity is one of those topics that turns “electricity” from something mysterious into something measurable. Change the length, change the area, change the material, change the temperature — and the circuit responds in a predictable way. Physics, basically, is just the universe being politely consistent.