Inverse Variation

Question

The resistance, R (in ohms), of a wire varies directly with the length , L (in cm), of the wire, and inversely with the cross-sectional area, A (in cm^2). A 500 cm piece of wire with a radius of 0.2 cm has a resistance of 0.025 ohm. Find an equation that relates these variables.

Answer 1

R = k*L/A

k = constant

L=length

A=area

0.025 ohms = k (500cm / (π*(0.2cm)²))

Solve for k (k=6.28x10^-6 ohms*cm)

Thus, R = 6.28x10^-6 * L/A (length in cm, area in cm²)