A piece of Nichrome wire has a radius of 7.1 x 10-4 m. It is used in a laboratory to make a heater that dissipates 3.20*102 W of power when connected to a voltage source of 110 V. Ignoring the effect of temperature on resistance, estimate the necessary length of wire.

the length of the Nichrome wire is 59.88 m

Explanation:

The resistance of a wire is determined by:

P = V² / R or R = V² / P

where

V is the voltage R is the resistance P is the power

We also know that

R = PL / A

where

A is the area and it is equal to πr² P = 3.20 * 10² W

Therefore, the length of the Nichrome wire is

L = RA / ρ

L = (V²/P) (πr²) / ρ

L = V²πr² / ρ P

L = (110 V) ² (π) (7.1 * 10⁻⁴ m) ² / (3.2 * 10² W) (100 * 10⁻⁸ Ω·m)

L = 59.88 m