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AP Physics C: E&M
11.3 Resistance, Resistivity, and Ohm’s Law
AdvancedMCQMathematicalConceptual22.3k
Coaxial resistor with radial current flow.
Coaxial resistor with radial current flow.
A cylindrical resistor of length \(L\) consists of a weakly conducting material filling the region between an inner cylindrical conductor of radius \(a\) and a coaxial outer cylindrical conductor of radius \(b\). The material has a non-uniform resistivity that depends on the radial distance \(r\) from the central axis according to \(\rho(r) = \rho_0 \left(\dfrac{r}{a}\right)^2\), where \(\rho_0\) is a positive constant. A potential difference is established between the two conductors such that current flows radially outward. Which of the following expressions represents the correct integral setup to determine the total electrical resistance \(R\) between the inner and outer cylindrical surfaces?

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