Question
The resistivity of aluminum is $2.8 \times 10^{-8} \Omega \cdot \mathrm{m}$. How long a piece of aluminum wire $1.0 \mathrm{~mm}$ in diameter is needed to give a resistance of $4.0 \Omega$ ?
Step 1
The radius is half of the diameter. Given that the diameter is 1.0 mm, the radius will be 0.5 mm. We also need to convert this radius from millimeters to meters, which gives us $0.5 \times 10^{-3}$ m. Show more…
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Number 10 wire has a diameter of $2.59 \mathrm{~mm}$. How many meters of number 10 aluminum wire are needed to give a resistance of $1.0$ $\Omega ? \rho$ for aluminum is $2.8 \times 10^{-8} \Omega \cdot \mathrm{m}$. From $R=\rho L / A$ $$ L=\frac{R A}{\rho}=\frac{(1.0 \Omega)(\pi)\left(2.59 \times 10^{-3} \mathrm{~m}\right)^{2} / 4}{2.8 \times 10^{-8} \Omega \cdot \mathrm{m}}=0.19 \mathrm{~km} $$
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