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

a is the right answer