Question

Calculate the ratio of the resistance of 10.0 m of aluminum wire 2.4 mm in diameter, to 28.0 m of copper wire 1.7 mm in diameter. The resistivity of copper is1.68×10−8Ω⋅m and the resistivity of aluminum is 2.65×10−8Ω⋅m.

Answer 1

Resistance R is given by

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

where l is length and A is area and $\rho$ is resistivity.

so for aluminium radious r= 1.2 m

$R_{a}=(2.65\times 10^{-8})\times \frac{10.0}{\pi \times (1.2)^{2}}$

For copper r= (1.7) / 2 =0.85 m

$R_{c}=(1.68\times 10^{-8})\times \frac{28}{\pi \times (0.85)^{2}}$

Ration

$\frac{R_{a}}{R_{c}}= \frac{\frac{10\times 2.65\times 10^{-8}}{\pi \times (0.0012)^{2}}}{\frac{28\times 1.68\times 10^{-8}}{\pi \times (0.00085)^{2}}}$

$\frac{R_{a}}{R_{c}}= 0.283$