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 cm2). 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.

R = 2π*10⁻⁶ L / A

Step-by-step explanation:

Resistance varies directly with length and inversely with area, so:

R = kL/A

A round wire has cross-sectional area of:

A = πr²

Substituting:

R = kL / (πr²)

Given that R = 0.025 Ω when L = 500 cm and r = 0.2 cm:

0.025 = k (500) / (π (0.2²))

k = 2π*10⁻⁶

Therefore:

R = 2π*10⁻⁶ L / A