Question

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

Answer 1

Since the resistivity of alloy is greater than the resistivity of its constituents. We have resistivity of manganin greater than resistivity of copper metal.

 So, Resistance `R = ρ1/A` 

Where l is length and A is area of cross-section of material.

Also ρ is the resistivity of the material.

For copper, `R_c = ρ_c l_c/A_c`

and for magnanin `R_m = ρ_m l_m/A_m`

We have

`ρ_m>ρ_c`

`or ρ_m/ρ_c > 1`

`As  l_c = l_m`

Dividing `R_c/R_m = (ρ_cA_m)/(ρ_mA_c)`

Again `R_c = R_m`

`therefore ρ_c A_m = ρ_mA_c`

`ρ_m/ρ_c=A_m/A_c >1`

Hence `A_m >A_c`

Or, Manganin wire is thicker.