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AP Physics 2
11.4 Electric Power
11.3 Resistance, Resistivity, and Ohm’s Law
AdvancedMCQMathematicalProportional AnalysisConceptual20.7k
Cylindrical transmission cables X and Y with specified dimensions and material resistivities carrying equal currents.
Cylindrical transmission cables X and Y with specified dimensions and material resistivities carrying equal currents.
Two cylindrical transmission cables, Cable X and Cable Y, are composed of different conductive alloys. Cable X has length \(L_0\), circular cross-sectional radius \(r_0\), and material resistivity \(\rho_0\), while Cable Y has length \(2L_0\), circular cross-sectional radius \(2r_0\), and material resistivity \(3\rho_0\). Both cables carry the same steady direct current \(I_0\) distributed uniformly across their cross sections. Which row in the table correctly compares the electrical resistance \(R_Y / R_X\), the internal electric field magnitude \(E_Y / E_X\), and the rate of thermal energy dissipation \(P_Y / P_X\) of Cable Y to Cable X?

Resistance Ratio (\(R_Y / R_X\))Electric Field Ratio (\(E_Y / E_X\))Power Dissipation Ratio (\(P_Y / P_X\))
Row A\(3\)\(\dfrac{3}{2}\)\(3\)
Row B\(\dfrac{3}{2}\)\(\dfrac{3}{2}\)\(\dfrac{3}{2}\)
Row C\(\dfrac{3}{2}\)\(\dfrac{3}{4}\)\(\dfrac{2}{3}\)
Row D\(\dfrac{3}{2}\)\(\dfrac{3}{4}\)\(\dfrac{3}{2}\)

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