A resistor is constructed by shaping a material of resistivity p into a hollow c

Question

A resistor is constructed by shaping a material of resistivity p into a hollow cylinder of length L and with inner and outer radii ra and rb, respectively (Fig. P27.66). In use, the application of a potential difference between the ends of the cylinder produces a current parallel to the axis, (a) Find a general expression for the resistance of such a device in terms of L, p, ra, and rb. (b) Obtain a numerical value for. R when L = 4.00 cm, ra = 0.500 cm, rb = 1.20 cm, and p = 3.50 times 105 Ohm m. (c) Now suppose that the potential difference is applied between the inner and outer surfaces so that the resulting current flows radially outward. Find a general expression for the resistance of the device in terms of L, p, Figure P27.66 ra, and rb. (d) Calculate the value of R, using the parameter values given in part (b).

Explanation / Answer

resistance of the wire is l/A where l is the length of the wire parallel to the current A is area of the wire perpendicular to the current hence a)l/(Rb2-Ra2) b)calculate c)we need to integrate here as area is varying dR=dx/l*2x we need to integrate this between R1 and R2 we get ln(R2/R1)/l*2 d)calculate

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