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(III) A hollow cylindrical resistor with inner radius r1 and outer radius r2, and length ℓ, is made of a material whose resistivity is ρ (Fig. 25–36). (a) Show that the resistance is given by
for current that flows radially outward. [Hint: Divide the resistor into concentric cylindrical shells and integrate.] (b) Evaluate the resistance R for such a resistor made of carbon whose inner and outer radii are 1.0 mm and 1.8 mm and whose length is 2.4 cm. (Choose ρ = 15 × 10−5 Ω · m.) (c) What is the resistance in part (b) for current flowing parallel to the axis?
FIGURE 25–36 Problem 30.
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