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AP Physics 2
11.3 Resistance, Resistivity, and Ohm’s Law
AdvancedMCQProportional AnalysisConceptual18.4k
A 3D perspective line drawing of a hollow cylindrical tube of length L aligned horizontally along a central axis. The left circular face shows an inner circular opening of radius r_1 and an outer boundary of radius r_2. Dashed lines indicate the inner cylindrical wall running along the length L. Two electrical wires extend from the left and right flat ends of the hollow tube, connecting to a DC voltage source labeled V_0. An arrow along the central axis indicates the direction of conventional current from left to right. No other labels, lines, text, or axes appear.
A hollow cylindrical resistor connected to a voltage source.
A resistor consists of a hollow cylinder of resistivity \(\rho\), length \(L\), inner radius \(r_1\), and outer radius \(r_2\). Conductive end caps are attached to both circular ends, connecting the resistor to an ideal battery that maintains a constant potential difference \(V_0\) across its length, producing a total current \(I_1\) and a uniform current density \(J_1\). A second resistor of the same length \(L\) and resistivity \(\rho\) is constructed with inner radius \(2r_1\) and outer radius \(2r_2\), and is connected across the same potential difference \(V_0\). Which of the following correctly compares the total current \(I_2\) to \(I_1\) and the magnitude of the current density \(J_2\) to \(J_1\)?

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