Question

Suppose that you wish to fabricate a uniform wire out of1.15 g of copper. Assume the wire has aresistance R = 0.300 , and all ofthe copper is used.

(a) What will be the length of the wire?

(b) What will be the diameter of the wire?

Answer 1

(a) L = 149.2 cm

(b) d = 0.033 cm

Step-by-step explanation:

Note that the resistivity of copper is

`\rho = 1.72* 10^(-8)~{\rm \Omega . m} = 1.72* 10^(-6)~{\rm \Omega.cm}`

and the mass density of copper is

`d = 8.96~{\rm g/cm^3}`

We will use the following formula to relate the resistance to other parameters

`R = (\rho L)/(A) = (\rho L)/(\pi r^2)`

If all the copper with 1.15 g is used, then

`m = dV\\1.15 = 8.96 * (L\pi r^2)\\L\pi r^2 = 0.128`

Back to the resistance:

`0.3 = (1.72* 10^(-6) L)/(\pi r^2)\\L = \pi r^2 (1.74* 10^5)\\L = (0.128)/(L)(1.74* 10^5)\\L = 149.2~{\rm cm}`

Then, the diameter is

`149.2* \pi r^2 = 0.128\\r = 0.0165~{\rm cm}\\d = 2r = 0.033~{\rm cm}`