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title: "Two rectangular conducting slabs, 1 and 2, have identical length \\(L\\), width \\(w\\), and thickness \\(t\\). Both slabs carry a steady current \\(I\\) in the \\(+x\\)-direction from \\(x = 0\\) to \\(x = L\\). The resistivity of Slab 1 is given by \\(\\rho_1(x) = \\rho_0\\left(1 + \\dfrac{x}{L}\\right)\\) and the resistivity of Slab 2 is given by \\(\\rho_2(x) = \\rho_0\\left(1 + \\dfrac{x^2}{L^2}\\right)\\), where \\(\\rho_0\\) is a positive constant. Which of the following correctly compares the total resistance \\(R_1\\) of Slab 1 to \\(R_2\\) of Slab 2, and describes the concavity of the electric potential graph \\(V(x)\\) as a function of position inside Slab 1?"
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url: "https://nerd-notes.com/ubq/118386/"
date_modified: "2026-08-04T08:09:50+00:00"
---

# Two rectangular conducting slabs, 1 and 2, have identical length \(L\), width \(w\), and thickness \(t\). Both slabs carry a steady current \(I\) in the \(+x\)-direction from \(x = 0\) to \(x = L\). The resistivity of Slab 1 is given by \(\rho_1(x) = \rho_0\left(1 + \dfrac{x}{L}\right)\) and the resistivity of Slab 2 is given by \(\rho_2(x) = \rho_0\left(1 + \dfrac{x^2}{L^2}\right)\), where \(\rho_0\) is a positive constant. Which of the following correctly compares the total resistance \(R_1\) of Slab 1 to \(R_2\) of Slab 2, and describes the concavity of the electric potential graph \(V(x)\) as a function of position inside Slab 1?

Two rectangular conducting slabs, 1 and 2, have identical length \(L\), width \(w\), and thickness \(t\). Both slabs carry a steady current \(I\) in the \(+x\)-direction from \(x = 0\) to \(x = L\). The resistivity of Slab 1 is given by \(\rho_1(x) = \rho_0\left(1 + \dfrac{x}{L}\right)\) and the resistivity of Slab 2 is given by \(\rho_2(x) = \rho_0\left(1 + \dfrac{x^2}{L^2}\right)\), where \(\rho_0\) is a positive constant. Which of the following correctly compares the total resistance \(R_1\) of Slab 1 to \(R_2\) of Slab 2, and describes the concavity of the electric potential graph \(V(x)\) as a function of position inside Slab 1?

- **A.** \(R_1 < R_2\) | Concave up
- **B.** \(R_1 < R_2\) | Concave down
- **C.** \(R_1 > R_2\) | Concave down
- **D.** \(R_1 > R_2\) | Concave up

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118386/*