PhysicsBowl 2016 Q7

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PhysicsBowl 2016

7) In this question, we want to rank the magnitude of resistance of three resistors with the given specifications. Notice that we are varying the radius and the length of the resistor, so we get the intuition that a relationship between these variables could be useful.

Where L is length, A is cross-sectional area, R is resistance, ρ is resistivity, and r is radius of cross-section

From here, we can start by computing the magnitude of resistance for each resistor.

Where R is resistance, ρ is resistivity, L is length, and r is radius of cross-section

Let's pull out all constants to make the order apparent.

Where R is resistance, ρ is resistivity, L is length, and r is radius of cross-section

Finally, just ordering this from least to greatest.

Where R is resistance

Answer: E