Question

You want to design a portable electric blanket that runs on a 1.5 V battery. If you use copper wire with a 0.50 mm diameter as the heating element, how long should the wire be if you want to generate 15 W of heating power?

Answer 1

voltage V = 1.5 V
power P = 15 W
Resistance of the wire R = V^ 2/ P = 0.15 ohm
diameter d = 0.5 mm
radius r = d/ 2 = 0.25 mm
= 0.25 * 10 ^ -3 m
Area A = pi * r^ 2 = 1.96* 10 ^ -7 m^ 2
Resistivity of copper p = 1.68* 10 ^ -8 ohm - m
we know R = pL / A
from this length of the wire L = RA / p
plug the values we get L = 1.75 m