5.1.4

# Resistivity

Test yourself

## Resistivity

The resistivity of a material is a measure of how much resistance a material provides.

### Resistance to motion

• Resistance depends on the material of which the object is composed.
• Different materials offer different resistances to the flow of charge.
• Resistivity is an intrinsic property of a material, independent of its shape or size.

### Calculation

• The equation for resistivity is:
• Resistivity = (resistance x area) ÷ length
• ${\rho}=\frac{RA}{L}$
• Where ${\rho}$ is the resistivity, A is the area, R is the resistance and L is the length of the wire.

## Applications of Thermistors

Thermistors are electrical components which change their resistance based on their temperature. This means we can use thermistors in devices where outputs depend on temperature variation.

### Types of thermistors

• Thermistors come in two varieties: positive temperature coefficient and negative temperature coefficient thermistors.
• You only need to focus on negative temperature coefficient thermistors (NTC).

### NTC thermistors

• With negative temperature coefficient thermistors: the higher the temperature, the lower the resistance.
• The resistance is then a proxy (something used to reflect the value of a factor in a calculation) for the temperature of the thermistor.

## Determining the Resistivity of a Wire

We can perform the following experiment to determine the resistivity of a wire.

### Equipment

• First, determine the length of the wire (make sure the wire is straight) and the cross-sectional area using a micrometer screw gauge.
• The assumption with the micrometer screw gauge is that the wire's cross-sectional area is circular.
• Set up the wire with a flying lead that can be reattached at any arbitrary (random) point on the wire.
• Make sure that the current used is low otherwise the wire will heat up and the results will inflate the resistivity of the material.

### Method

• Record the resistance for various lengths of wire.
• The resistance can be determined by the ratio of observed potential difference to observed current.
• Plot resistance (y-axis) against the length of the wire (x-axis).
• Determine the gradient of the graph and multiply the gradient by the cross-sectional area to find the resistivity of the wire.