Resistance and Resistivity problem

[Snowman2526]

Homework Statement

A piece of Nichrome wire has a radius of 8.6 x 10^-3 m. It is used in a laboratory to make a heater that dissipates 575 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.

Nichrome wire had resistivity of 100x10^-8

Homework Equations

p=resistivity
P=power
L=length of wire
A=cross sectional area of wire
I=Current
V=Voltage

R=pL/A
R=V/I
P=IV

The Attempt at a Solution

I first solved for current, since i'd need to plug resistance into the first equation to make L the only unknown. So P/V=I gives I=4.792 Amperes. Then I needed to take the radius of the wire and make it into cross sectional area, so A=(pi)r^2...A=.000232 m^2.

Now to solve the first equation for L...L=pV/IA.

L=(100x10^-8 ohm-m)(120 V)/(4.792 A)(.000232 m^2)


now, i know I'm getting the wrong answer of .1079 m. can anyone tell me what I'm doing wrong?

 

[tiny-tim]

Hi Snowman2526!

(have a rho: ρ )

Now to solve the first equation for L...L=pV/IA.

Noooo … ρ = (A/L)(V/I), so L = … ?

 

[Snowman2526]

thank you sir :) problem solved