Conductor Resistance

#550 / Electrical & Computer Engineering Easy

Consider a 5 cm long cylindrical conductor has an electrical resistivity of 0.002 Ω∙m and a resistance of 1 Ω. What is its diameter in mm?

Expand Hint
A conductor’s resistance:
$$$R=\frac{\rho L}{A}$$$
where $$\rho$$ is the electrical resistivity, $$L$$ is the conductor’s length, and $$A$$ is the cross sectional area.
Hint 2
Area of a circle:
$$$A=\frac{\pi}{4}D^2$$$
where $$D$$ is the diameter.
A conductor’s resistance:
$$$R=\frac{\rho L}{A}$$$
where $$\rho$$ is the electrical resistivity, $$L$$ is the conductor’s length, and $$A$$ is the cross sectional area.

Solving for area:
$$$1\Omega=\frac{(0.002\Omega\cdot m) (0.05m)}{A}$$$
$$$A=\frac{(0.0001m^2)}{1}=0.0001\:m^2$$$
Area of a circle:
$$$A=\frac{\pi}{4}D^2$$$
where $$D$$ is the diameter.
$$$0.0001m^2=\frac{\pi}{4}D^2$$$
$$$D^2=1.27\times10^{-4}m^2$$$
$$$D=\sqrt{1.27\times10^{-4}m^2}=0.01128\:m=11.3\:mm$$$
11.3 mm


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