Physics Help Please!

Question

The wiring in a house must be thick enough so it does not become so hot as to start a fire. What diameter must a copper wire be if it is to carry a maximum current of 39 A and produce no more than 1.5 W of heat per meter of length?

Answer 1

Hi Again,

The resistivity of copper wire is ρ = 1.724 x 10-8 Ω·m

 

Let A be the cross-sectional area of the copper wire

 

A = Π r²

The power (P) produced by current I through a copper wire of resistance  R  and length L is given by

P*L = I²R

(1.5 W/m) *L = (39A)² R        

 

(1.5W/m)/(39A)² = R/L    Giving  R/L = 9.862 x10^-4 Ω/m

 

R =ρL/A 

 

R/L = ρ/A 

 

9.862x10^-4 Ω/m= 1.724x10^-8 Ω·m/Π r²

 

r²  = 1.724x10^-8/(Π *9.862x10^-4) = 5.564x10^-6

 

r =2.359x10^-3m or 0.2359 cm   diameter d = 2*r

 

The diameter is 0.47cm