12 A wire-wound resistor consists of a long length of wire wound around an insulating core - Edexcel - A-Level Physics - Question 12 - 2023 - Paper 1

To determine the length of the wire, we use the formula for resistance:

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

where:

• $R$ is the resistance (80 Ω)
• $\rho$ is the resistivity of the material (4.9 × 10⁻⁸ Ω m)
• $L$ is the length of the wire
• $A$ is the cross-sectional area of the wire.

First, we calculate the cross-sectional area ($A$) of the wire: The diameter of the wire is 0.28 mm, which is 0.00028 m. Thus, the radius $r$ is:

$r = \frac{0.28}{2} \times 10^{-3} = 0.00014 \, \text{m}$

Now, using the formula for the area of a circle: $A = \pi r^2$

Substituting in the radius:

$A = \pi (0.00014)^2 \approx 6.16 \times 10^{-8} \, \text{m}^2$

Next, we can rearrange the resistance formula to solve for $L$:

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

Substituting in the values:

$L = \frac{80 \cdot 6.16 \times 10^{-8}}{4.9 \times 10^{-8}} \approx 100.0 \, \text{m}$

Thus, the length of the constantan wire used to make the resistor is approximately 100.0 meters.