Define (i) resistance, (ii) resistivity - Leaving Cert Physics - Question 9 - 2007

Resistivity is an intrinsic property of a material, defined as the resistance of a unit cube of that material. It can be expressed mathematically as:

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

where:

• $\rho$ is the resistivity,
• $R$ is the resistance,
• $A$ is the cross-sectional area,
• $L$ is the length of the material.

To calculate the resistance $R$ of the nichrome wire, we can use the formula:

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

Where:

• $\rho$ for nichrome wire is given as approximately $1.36 \times 10^{-6} \Omega \cdot m$,
• $L = 220 \ mm = 0.22 \ m$,
• $A = \pi r^2 = \pi (0.055 \ mm)^2 =\pi (0.055 \times 10^{-3})^2.$

After calculating, we find:

$R \approx 7.86 \Omega.$

Using the earlier formula for resistivity:

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

Substituting values:

• $R = 7.86 \Omega$,
• $A = \pi (0.055 \times 10^{-3})^2$,
• $L = 0.22 \ m$.

This yields:

$\rho \approx 1.36 \times 10^{-6} \Omega \cdot m.$

The graph should be a straight line starting from the origin (0,0) that slopes upwards to the right. This represents that as the temperature increases, the resistance of the nichrome wire also increases. The slope may vary, reflecting the material's characteristics.

As the temperature of the wire falls below 0°C, the resistance generally increases, as most conductors will experience increased resistance at lower temperatures.

As the length of the wire increases, the resistance increases proportionally, as resistance is directly proportional to length. This can be expressed as:

$R \propto L$.

If the diameter of the wire is increased, the resistance decreases. This is because the cross-sectional area increases and resistance is inversely proportional to the area:

$R \propto \frac{1}{A}$.

Another device that can be used to measure resistance is an ohmmeter.

One advantage of using an ohmmeter is that it is portable and easy to use, allowing for quick measurements. However, a disadvantage is that it may not provide as accurate readings as a metre bridge, especially for low resistance values.