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AP Physics C: E&M
11.3 Resistance, Resistivity, and Ohm’s Law
11.1 Electric Current
AdvancedMCQGraphicalMathematicalConceptual23.7k
A horizontal cylindrical rod of uniform thickness lies along the horizontal axis, extending from a vertical dashed reference line labeled \(x = 0\) on the left to a vertical dashed reference line labeled \(x = L\) on the right. A shading gradient fills the rod, being light gray at \(x = 0\) and darkening continuously toward dark gray at \(x = L\). An ideal battery labeled \(V_0\) is shown below the rod. A solid wire connects the longer, positive plate of the battery to the left end of the rod at \(x = 0\). A second solid wire connects the shorter, negative plate of the battery to the right end of the rod at \(x = L\), where a three-line ground symbol is attached. A horizontal coordinate arrow below the rod points to the right and is labeled \(x\). No other labels, lines, text, or axes appear.
A rod with position-dependent resistivity connected across an ideal battery of potential difference \(V_0\).
A cylindrical conducting rod of length \(L\) and uniform cross-sectional area \(A\) is oriented along the \(x\)-axis from \(x = 0\) to \(x = L\). The rod is composed of an inhomogeneous material whose resistivity varies with position according to \(\rho(x) = \rho_0\left(1 + \dfrac{x}{L}\right)\), where \(\rho_0\) is a positive constant. An ideal battery maintains the end at \(x = 0\) at electric potential \(V_0\) while the end at \(x = L\) is grounded at zero potential. Which of the following graphs best represents the electric potential \(V\) as a function of position \(x\) along the rod?

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