Question

A piece of silver wire has a resistance of 1.0Ω. What will be the resistance of a manganin wire; 

one-third the length and one-third the diameter if the resistivity of manganin is 30 times that of silver.

Answer 1

For aluminium wire

Resistance=R

Length=L

Resistivity=$\rho$

Diameter=D

Area (A)=$\frac{\pi D^2}{4}$

For mangnin wire

Resistance=R'

Length(L')=$\frac{L}{3}$

Resistivity ($\rho'$ )=$30\rho$

Diameter D'=$\frac{D}{3}$

$R=\frac{\rho l}{A}$

Area(A')=$\frac{\pi D^2}{36}$

$\frac{R'}{R}=\frac{\frac{30\rho\times{\frac{L}{3}}}{\frac{\pi D^2}{36}}}{\frac{\rho\times{L}}{\frac{\pi D^2}{4}}}$

$\frac{R'}{R}=90\\R'=90R$