A particular wire has a resistivity of 6.47*10-8 Ωm and a cross-sectional area of 2.32 mm2. A length of this wire is to be used as a resistor that will develop 130 W of power when connected to a 9.00 V battery. What length of wire is required?

Using the formula for power:

P = V^2 / R

130 W = (9.00 V) ^2 / R

Solve for r:

R = 81/130

R = 0.623 ohms

Now solve for the length of wire:

R = rho L / A

A must be in m^2 - 2.32 mm^2 * 1 m^2/10^6 mm^2 = 2.132x10^-6 m^2

Now you have:

0.623 = (6.47x10^-8) L / (2.32x10^-6)

L = 22.34 m (Round answer as needed.)