IMAT 2018 Q58 [Electrical Resistance]

A wire made of a metal of uniform resistivity 1.0 × 10^{–6} Ω m is 2.0 m long and has a diameter of 2.0 × 10^{–3} m.

What is the electrical resistance of this length of the wire?

A. \frac{2.0 \times 10^{-3}}{\pi} Ω

B. 5.0 \times 10^{-13} \pi Ω

C. \frac{1.0}{2\pi} Ω

D. 2.0 \times 10^{-12} \pi Ω

E. \frac{2.0}{\pi} Ω

In order to solve this we must know the equation representing the dependency of the resistance (R) of a cylindrically shaped conductor (e.g., a wire) upon the variables that affect it is: R = p\frac{L}{A},
where L represents the length of the wire (in meters), A represents the cross-sectional area of the wire (in meters2) and p represents the resistivity of the material (in ohm meter).

Using this, we can calculate: R = 1 \cdot 10^{-6}\Omega m \frac{2 m}{\pi \cdot (\frac{1}{2} 2 \cdot 10^{-3})^2} = \frac{2 \cdot 10^{-6}}{\pi \cdot 1 \cdot 10^{-6}} \Omega = \frac{2.0}{\pi}\Omega.

So the final answer is (E)

ps. a diameter is given, to get the radius of the wire we must divide the diameter by 2

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