Question

A 40ohm resistor is to be wound from platinum wire 0.1mm in diameter.How much wire is needed?

Answer 1

You have to state the resistivity of the Platinum.
but we can consider it at the standard value (1.06×10−7 Ω·m)

Diameter = 0.1 mm , So radius = 0.05 mm = 0.00005 meter

\[R = \rho {L \over A} = \rho {L \over \pi r^2}\]

\[R = 1.06 \times 10^{-7} \times {L \over 5 \times 10^{-5} \times \pi} = 40\]

\[L = { 40 \times 5 \times 10^{-5} \times \pi \over 1.06 \times 10^{-7} } = 59275.33 \ \ meters\]