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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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