Question

If 18 meters of high-resistance wire with a diameter of 1.2 mm has a resistance of 10 ohms, what is the resistance of 27 m of the same type of wire with a diameter of 1.5 mm?

Answer 1

The resistance is proportional to length and inversely proportional to the cross sectional area.
Increasing the length while keeping the diameter the same we get\[R _{1}=\frac{10}{18}\times 27\ ohms\]
The cross sectional area is proportional to the square of the diameter, so increasing the diameter of the 27 m length to 1.5 mm gives the following resistance:
\[R _{2}=\frac{10}{18}\times 27\times \frac{(1.2)^{2}}{(1.5)^{2}}\ ohms\]