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 1.5mm?

The electrical resistance of a wire varies as its length and inversely as the square of the diameter.

R = (k*L) / (d^2)

where k = proportionality constant

Since the two wires have the same material, their proportionality constant is same.

Equating that

(R1*d1^2) / L1 = (R2*d2^2) / L2

Given that R1 = 10 ohms, d1 = 1.2 mm or 0.0012 m, L1 = 18 m, d2 = 1.5 mm or 0.0015 m, L2 = 27 m, and R2 is unknown.

Therefore

[10 * (0.0012^2) ]/18 = [R2 * (0.0015^2) ]/27

R2 = 9.6 ohms