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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