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Resistance and Resistivity problem

  • #1

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?
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,832
249
Hi Snowman2526! :wink:

(have a rho: ρ :wink:)
Now to solve the first equation for L.....L=pV/IA.
Noooo … ρ = (A/L)(V/I), so L = … ? :smile:
 
  • #3
thank you sir :) problem solved
 

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