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AP Physics C: E&M
11.6 Kirchhoff’s Loop Rule
11.3 Resistance, Resistivity, and Ohm’s Law
11.1 Electric Current
AdvancedMCQGraphicalMathematicalConceptual19.5k
Two cylindrical resistors connected in series carrying steady current \(I\).
Two cylindrical resistors connected in series carrying steady current \(I\).
A cylindrical resistor of length \(L\) and uniform cross-sectional area \(A\) has a position-dependent resistivity given by \(\rho(x) = \rho_0\left(1 + \dfrac{x}{L}\right)\) for \(0 \le x \le L\), where \(\rho_0\) is a positive constant. It is connected in series at \(x = L\) to a second cylindrical resistor of the same cross-sectional area \(A\), length \(L\), and uniform resistivity \(2\rho_0\) occupying the interval \(L \le x \le 2L\). A steady current \(I\) flows through the combination in the \(+x\)-direction, and the end at \(x = 2L\) is connected to an electrical ground such that \(V(2L) = 0\text{ V}\).

Which of the following best describes the graph of the electric potential \(V(x)\) as a function of position \(x\) for \(0 \le x \le 2L\)?

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