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in Physics by (56.9k points)

Two cylindrical resistors are made of the same material and have the same resistance. The resistors, R1 and R2, have different radii, r1 and r2, and different lengths, L1 and L2. Which of the following relative values for radii and lengths would result in equal resistances?

(1) 2r1 = r2 and 4L1 = L2 

(2) 2r1 = r2 and L1 = 2L2 

(3) r1 = r2 and 4L1 = L2 

(4) r1 = r2 and L1 = 2L2 

(5) none of these

1 Answer

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Best answer

Correct option: (4) r1 = r2 and L1 = 2L2

Explanation:

The resistance is given by R = ρL / A , where ρ is the resistivity, L is the length and A is the cross sectional area. To keep R unchanged, the ratio of L to A must be unchanged. Since A = πr2 , if r is doubled then L must be multiplied by 

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