An aluminum rod with a square cross section is 1.3 m long and 5.3 mm on edge. (a) What is the resistance between its ends? (b) What must be the diameter of a cylindrical copper rod of length 1.3 m if its resistance is to be the same as that of the aluminum rod? The resistivity of aluminum is 2.75 × 10^-8 Ω·m and the resistivity of copper is 1.69 × 10^-8 Ω·m.

To find the resistance of the aluminum rod, we can use the formula R = ρL/A, where R is resistance, ρ is resistivity, L is length, and A is cross-sectional area. The cross-sectional area of the aluminum rod can be found by squaring the edge length. Plugging in the values, we get R = (2.75 × 10-8 Ω·m)(1.3 m)/ (5.3 × 10-3 m)2. Simplifying this equation, we find the resistance is 4.76 × 10-3 Ω.

To find the diameter of the copper rod, we can use the same formula. We want the resistance of the copper rod to be the same as the resistance of the aluminum rod, so we can set up the equation (2.75 × 10-8 Ω·m)(1.3 m)/(AAl) = (1.69 × 10-8 Ω·m) (1.3 m)/((π/4) (dCu)2), where AAl is the cross-sectional area of the aluminum rod and dCu is the diameter of the copper rod. Rearranging the equation and solving for dCu, we find that the diameter of the copper rod must be 5.63 mm.

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