A piece of Nichrome wire has a radius of 62 x 104 m It is us

A piece of Nichrome wire has a radius of 6.2 x 10-4 m. It is used in a laboratory to make a heater that dissipates 4.80×102 W of power when connected to a voltage source of 140 V. Ignoring the effect of temperature on resistance, estimate the necessary length of wire.

Solution

Given:
r=6.2*10^-4 m
P=4.8*10^2 W
V=140V

Find the current needed to produce 480W from 140V:
P=(I^2)*R=V*I=(V^2)/R
so R= V^2/P = 140*140/480 =40.833 ohm

Using the electrical resistivity of Nichrome (=1.10×106 *m at 20°C) and the cross-sectional area (A=*r^2), find the length (x) of wire:
=R*A/x
x=R*A/ = 40.833*3.14*6.2*6.2*10^-4*10^-4/(1.1 * 10^-6) = 44.80m