ELECTROMAGNETISM & RELATIVITY - Chapter 3, Exercise 2 Solution
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Resistance of a Copper Wire

PROBLEM
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A copper wire has a resistivity of 1.68 x 10^-8 ohm.m, a length of
5 m, and a cross-sectional area of 2 x 10^-6 m^2. Calculate its
resistance.

SOLUTION
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Using the wire resistance formula:

    R = rho L / A

Substitute the given values:

    rho = 1.68 x 10^-8 ohm.m
    L = 5 m
    A = 2 x 10^-6 m^2

    R = (1.68 x 10^-8 x 5) / (2 x 10^-6)
    R = (8.4 x 10^-8) / (2 x 10^-6)
    R = 0.042 ohms

ANSWER: The wire's resistance is 0.042 ohms.

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WHY THIS WORKS AS AN ANSWER

The formula R = rho L / A captures two real, independent geometric
effects at once: resistance increases with length (a longer wire
gives charge carriers a longer path to travel through, encountering
more resistance along the way), and resistance decreases with a
larger cross-sectional area (a thicker wire gives charge carriers
more room to flow through in parallel, effectively acting like many
thinner wires side by side). This wire's own very low resistance
(0.042 ohms) is typical of real copper wiring at everyday lengths -
exactly why copper is the standard choice when minimizing wasted
power (P = I^2 R) in household and electronic wiring matters.