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

`L=4.8*10^(17)m`

Step-by-step 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=(V_(2))/(R)\\ R=(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=(RA)/(p)\\ L=(((V^(2)))/(P)(\pi r^(2)) )/(p) \\L=(V^(2)(\pi r^(2)))/(pP)\\ L=((120V)^(2)\pi (6.5*10^(4) m)^(2) )/(100*10^(-8)(4.00*10^(2) W) )\\ L=4.8*10^(17)m`