Question

A piece of Nichrome wire has a radius of 6.5 104 m. It is used in a laboratory to make a heater that uses 4.00 102 W of power when connected to a voltage source of 120 V. Ignoring the effect of temperature on resistance, estimate the necessary length of wire.

Answer 1

Answer:

$L=4.8*10^{17}m$

Explanation:

Given data

Power P=4.00×10²W

Radius r=6.5×10⁴m

Voltage V=120V

To find

Length of wire L

Solution

We know that resistance of wire can be obtained from

$P=\frac{V_{2}}{R}\\ R=\frac{V_{2}}{P}$

We also know that R=pL/A solving the length noting that A=πr²

and using p=100×10⁻⁸Ω.m we find that

So

$L=\frac{RA}{p}\\ L=\frac{\frac{(V^{2})}{P}(\pi r^{2}) }{p} \\L=\frac{V^{2}(\pi r^{2})}{pP}\\ L=\frac{(120V)^{2}\pi (6.5*10^{4} m)^{2} }{100*10^{-8}(4.00*10^{2} W) }\\ L=4.8*10^{17}m$