AP Physics C: E&M
11.3 Resistance, Resistivity, and Ohm’s Law
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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