Answer to Question #176464 in Electric Circuits for Kanda Gideon

Question

Find the diameter of copper wire with which it has the same resistance as aluminium wire of equal length and diameter 1.20mm. The resistivity of copper and aluminum at room temperature are 1.7×10^-8ohms per meter and 2.6× 10^-8ohms per meter respectively

Answer 1

To be given in question

R_Al=R_cu

L_Al=L_cu

Aluminium wire diameter D(Al)=1.20mm

Resistivity copper wire$\rho$ (cu)=1.7$\times$ $10^{-8}$ ohm/meter

Resistivity aluminium wire $\rho$ (Al)=2.6$\times$ $10^{-8}$ ohm/meter

To be asked in question

Diameter of copper wire D(cu)=?

Formula $R=\frac{\rho L}{A}$

=R_Al=R_cu

[$\frac{\rho L}{A}$ ]_Al=[ $\frac{\rho L}{A}$ ] _cu

Both wire length are equal

$[\frac{\rho }{A}] (Al) =[\frac{\rho }{A}](cu)$

Put value 

$[\frac{2.6\times10^{-8}\times4}{\pi\times[ 1.20\times 10^{-3}]^2}]= [\frac{1.7\times10^{-8}\times4}{\pi\times [D^{2}(cu)]}]$

$= 9.703 \times 10^{-04} meter$