Question

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

Answer 1

Resistance $R$ of a wire of length $l$ and cross sectional area $A$ (thickness) is given by ,

$R=\rho l/A$

where $\rho =$ specific resistance of wire

for copper wire $R={\rho }_{c}l/A_c$ ,

for manganin wire $R={\rho }_{m}l/A_m$

or ${\rho }_c/A_c={\rho }_m/A_m$

or $A_c/A_m={\rho }_c/{\rho }_m$

we know ${\rho }_m>{\rho }_c$ (as manganin is an alloy)

therefore $A_c<A_m$

Hence manganin wire is thicker.