Answer to Question #175803 in Electric Circuits for Joshua Musyoki

Question

. Find the diameter of a copper wire which has the same resistance as aluminium wire of equal 

length and diameter 1.20mm. The resistivities of copper and aluminium at room temperature are 

1.7 × 10−8Ω𝑚 and 2.6 × 10−8Ω𝑚 respectively. 

Answer 1

Answer

Resistance is given

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

Relation between area and diameter

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

So final relation is given

$D=\sqrt{\frac{4\rho l}{\pi R}}$

$D_a=D_c\sqrt{\frac{\rho _a}{\rho _c}}\\=(0.0012)\sqrt{\frac{ 2.6× 10^{−8 } }{ 1.7× 10^{−8 }}}\\=1.5mm$