What diameter of copper wire (p=2.65x10-8ohm x m) should be used so that a 22.0

Question

What diameter of copper wire (p=2.65x10-8ohm x m) should be used so that a 22.0 m length will have a resistance of 0.39 ohm? Find the temperature coefficient of resistivity for this wire if an increase of temperature of 120 C changes the resistance from .39 ohm to .62 ohm. What diameter of copper wire (p=2.65x10-8ohm x m) should be used so that a 22.0 m length will have a resistance of 0.39 ohm? Find the temperature coefficient of resistivity for this wire if an increase of temperature of 120 C changes the resistance from .39 ohm to .62 ohm.

Explanation / Answer

apply Resistance R = rho L/A

where L is length

A is area

rho is ressitivity of Copper 2.65 e-8 ohmm ( this is actually not Coppers)

so

Area A = rho L/R

A = pi r^2 = 2.65 e- 8 * 22/(0.39)

A = pi r^2 = 1.4948 e-6

r^2 = 1.4948/3.14 = 0.476 e -6

r = 0.689 mm

diameter   = 2r    =1.38 mm

-----------------------------
use the formula

Rt = Ro *(1+A dT)

here dT is the chnage of tempertature   = 120 deg C

so

1 + A dT = 0.62/0.39

AdT = 1.589 - 1

A = 0.580/120

A = 4.91 *10^-3 per deg C

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