Ask Question
8 July, 18:03

Find the resistance at 50°c of copper wire 2mm in diameter and 3m long

+3
Answers (1)
  1. 8 July, 18:09
    0
    0.0179 ohms for copper.

    0.0184 ohms for annealed copper

    Ď = R (A/l) where

    Ď = electrical resistivity

    R = electrical resistance of a uniform specimen

    A = cross sectional area

    l = length

    Solve for R by multiplying both sides by l/A

    R = Ď (l/A)

    The cross section of the wire is pi * 1^2 mm = 3.14159 square mm = 3.14159e-6 square meters.

    The length is 3 meters. So l/A = 3/3.14159e-6 = 9.5493e5

    Ď for copper is 1.68e-8 so 1.68e-8 * 9.5493e5 = 1.60e-2 ohms at 20 C

    But copper has a temperature coefficient (α) of 0.00386 per degree C.

    So the resistance value needs to be adjusted based upon how far from 20 C the temperature is.

    50 - 20 = 30 C

    So 0.00386 * 30 = 0.1158 meaning that the actual resistance at 50 C will be 11.58% higher.

    So 1.1158 * 0.016 = 0.0179 ohms.

    If you're using annealed copper, the values for Ď and the temperature coefficient change.

    Ď = 1.72e-8

    α = 0.00393

    Doing the math, you get

    1.72e-8 * 9.5493e5 * (1 + 30 * 0.00393) = 0.0184 ohms
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “Find the resistance at 50°c of copper wire 2mm in diameter and 3m long ...” in 📙 Physics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers