Two wire of equal lengths, one of copper and the other of manganin have the same resistance. Which wire is thicker?

Solution

Resistance is given by R= $ρ \frac{l}{A}$
The length and resistance of the wires are equal.

$\Rightarrow R_{1} = R_{2} \Rightarrow ρ_{1} \frac{l}{A_{1}} = ρ_{2} \frac{l}{A_{2}} \Rightarrow \frac{ρ_{1}}{ρ_{2}} = \frac{A_{1}}{A_{2}}$

Resistivity of Copper wire is less than that of the resistivity of magnanin wire. Therefore, the area of cross- section of copper wire is less than that of magnanin.
Hence, Manganin wire is thicker.

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Current Electricity

Two wire of equal lengths, one of copper and the other of manganin have the same resistance. Which wire is thicker?

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