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? A)r₁=r₂ and L₁= 2L₂ B)2r₁=r₂ and L₁= 2L₂ C)r₁=r₂ and 4L₁= L₂ D)2r₁=r₂ and 4L₁= L₂

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The resistance of a cylindrical resistor is given by R = ρ(L/A), where ρ is resistivity, L is length, and A is cross-sectional area (πr²). For equal resistances, ρ(L₁/πr₁²) = ρ(L₂/πr₂²). Simplifying gives L₁/r₁² = L₂/r₂². For choice D, substituting 2r₁ for r₂ and 4L₁ for L₂ satisfies this equation.

Two Cylindrical Resistors Are Made of the Same Material and Have