Two wires, one of copper and other of manganese have equal lengths and equal resistances: Which is thicker. (Given that resistivity of manganese is lower than that of copper).

Given: Two wires, one made of copper and other made of manganese have equal lengths and equal resistances. Resistivity of manganese is lower than that of copper

To find: Which wire is thicker.

Solution:

Copper wire should be thicker.

Length $l$ of both wires is same and their resistances are also equal.

So $\frac{\rho ( cu ) \times l }{ A (cu)} = \frac{\rho ( mn ) \times l }{ A (mn)}$ .

Canceling $l$ from both sides.

$\frac{A(mn)}{A(cu)} = \frac{\rho(mn) }{ \rho (cu)}$.

But $\rho (mn) < \rho (cu)$

So,  $\frac{A(mn) }{ A(cu)} < 1$.

This means $A(mn) < A(cu).$

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Updated on: 10-Oct-2022

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