Resistivity

Electrical Quanties

Define resistivity.

A property of a material that describes how strongly the material opposes the flow of electric current.

What is the symbol for resistivity?

ρ (rho).

What is the SI unit of resistivity?

Ohm metre (Ω m).

Does resistivity depend on the dimensions of a sample?

No. Resistivity is a property of the material itself.

What factors can affect the resistivity of a material?

The type of material and its temperature.

Do samples of the same material have the same resistivity at the same temperature?

Yes, regardless of their shape or size.

What is the difference between resistance and resistivity?

Resistance depends on the material and dimensions of a component, whereas resistivity is an intrinsic property of the material.

What equation links resistance and resistivity?

R = ρL/A.

What does R represent in R = ρL/A?

Resistance in ohms (Ω).

What does ρ represent in R = ρL/A?

Resistivity in ohm metres (Ω m).

What does L represent in R = ρL/A?

Length of the conductor in metres (m).

What does A represent in R = ρL/A?

Cross-sectional area of the conductor in square metres (m²).

How can resistivity be calculated?

ρ = RA/L.

How can the length of a conductor be calculated using resistivity?

L = RA/ρ.

How can cross-sectional area be calculated using resistivity?

A = ρL/R.

How does resistance depend on the length of a uniform conductor?

Resistance is directly proportional to length: R ∝ L.

Why does increasing the length of a wire increase its resistance?

Charge carriers travel further through the material and undergo more collisions.

What happens to resistance if the length of a wire is doubled?

The resistance doubles, provided the material, cross-sectional area and temperature remain constant.

How does resistance depend on the cross-sectional area of a conductor?

Resistance is inversely proportional to cross-sectional area: R ∝ 1/A.

Why does a thicker wire have a lower resistance?

It has a larger cross-sectional area, providing more pathways for charge carriers to flow.

What happens to resistance if the cross-sectional area of a wire is doubled?

The resistance halves, provided its material, length and temperature remain constant.

What happens to resistance if a wire's length is doubled and its cross-sectional area stays constant?

Its resistance doubles.

What happens to resistance if a wire's length is halved and its cross-sectional area stays constant?

Its resistance halves.

What happens to resistance if a wire's cross-sectional area is halved?

Its resistance doubles.

What is the equation for the cross-sectional area of a circular wire?

A = πr².

How is the radius of a wire found from its diameter?

r = d/2.

Why must wire diameter measurements be converted into metres when calculating resistivity?

Because resistivity uses SI units of Ω m and cross-sectional area must be in m².

What instrument is used to accurately measure the diameter of a thin wire?

A micrometer screw gauge.

Why should the diameter of a wire be measured at several positions?

To reduce random uncertainty and account for variations in the wire's diameter.

How should multiple measurements of wire diameter be used?

Calculate the mean diameter.

Why can measuring the diameter be a major source of uncertainty in a resistivity experiment?

The diameter is very small and the cross-sectional area depends on the square of the radius.

What happens to percentage uncertainty when a measured value is squared?

Its percentage uncertainty approximately doubles.

How can resistance of a wire be measured experimentally?

Measure the potential difference across the wire and current through it, then use R = V/I.

How is the ammeter connected in a resistivity experiment?

In series with the wire.

How is the voltmeter connected in a resistivity experiment?

In parallel across the measured length of wire.

How can the length of wire being tested be changed?

Move the contact along the wire to select different measured lengths.

Why should several different lengths of wire be tested?

To obtain multiple data points and allow a graph to be plotted, improving reliability.

What graph can be plotted in a resistivity experiment?

Resistance R on the y-axis against length L on the x-axis.

What relationship should an R against L graph show?

A straight-line relationship because R is directly proportional to L.

What is the gradient of a graph of resistance against length?

Gradient = ΔR/ΔL.

How is the gradient of an R against L graph related to resistivity?

Gradient = ρ/A.

How can resistivity be found from the gradient of an R against L graph?

ρ = gradient × A.

Why is using the gradient of an R against L graph better than calculating resistivity from one measurement?

It uses multiple measurements, reducing the effect of random uncertainty and giving a more reliable value.

What should the intercept of an ideal resistance against length graph be?

Zero.

Why might an experimental R against L graph have a non-zero intercept?

Additional resistance may come from connecting leads, contacts or other systematic errors.

Why should the current be kept low during a resistivity experiment?

To reduce heating of the wire.

Why is heating the wire a problem in a resistivity experiment?

Temperature changes the resistivity of the material.

What is a safety risk in a resistivity experiment?

A large current can make the wire hot enough to cause burns.

How can excessive heating of the wire be reduced?

Use a low current or voltage and switch the circuit off between measurements.

What happens to the resistivity of most metals when temperature increases?

Resistivity increases.

Why does the resistivity of a metal increase with temperature?

The metal ions vibrate more strongly, causing more frequent collisions with conduction electrons.

What does a low resistivity mean?

The material allows electric current to flow easily and is a good conductor.

What does a high resistivity mean?

The material strongly opposes current and is a poor conductor or insulator.

Why is copper commonly used for electrical wiring?

It has a very low resistivity and therefore conducts electricity well.

Which has lower resistivity: a typical metal or an insulator?

A typical metal.

What is conductivity?

A measure of how easily a material conducts electric current.

What is the relationship between conductivity and resistivity?

Conductivity is the reciprocal of resistivity.

What equation defines conductivity?

σ = 1/ρ.

What is the SI unit of conductivity?

Siemens per metre (S m⁻¹).

What does a high conductivity correspond to?

A low resistivity and good electrical conduction.

What does a low conductivity correspond to?

A high resistivity and poor electrical conduction.

If material A has a lower resistivity than material B, which is the better conductor?

Material A.

Why is constantan useful when an approximately constant resistance is required?

Its resistivity changes very little with temperature.

What three quantities must normally be measured to determine the resistivity of a wire experimentally?

The wire's resistance, length and cross-sectional area.

What measurements are needed to calculate the cross-sectional area of a wire?

Its diameter or radius.

How can uncertainty in the length measurement be reduced?

Use longer lengths of wire so the absolute measurement uncertainty is a smaller percentage of the measured length.

How can uncertainty in the wire diameter be reduced?

Take repeated micrometer measurements at different positions and orientations and calculate a mean.

How can uncertainty in resistance measurements be reduced?

Take measurements for several lengths and determine resistivity from the gradient of a best-fit graph.