Ranking Resistances of Cylindrical Resistors · PhysicsBowl 2016 #7

Physics · electromagnetism

Problem

Three cylindrical resistors are made of the same material. The length and radius of each resistor is: Resistor 1: Length LL, radius rr Resistor 2: Length L2\frac{L}{2}, radius r2\frac{r}{2} Resistor 3: Length L4\frac{L}{4}, radius r2\frac{r}{2} Which one of the following choices correctly ranks the resistance of these resistors (R1,R2,R3)(R_1, R_2, R_3)? (A) R1=R2<R3R_1 = R_2 < R_3 (B) R2<R1<R3R_2 < R_1 < R_3 (C) R3<R2<R1R_3 < R_2 < R_1 (D) R1<R2=R3R_1 < R_2 = R_3 (E) R1=R3<R2R_1 = R_3 < R_2

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