Mon May 23, 2011 By: M. Bhanu Ashwin

Find the resistance of a hollow cylindrical pipe of length 1m whose inner and outer radii are 10cm and 20 cm respectively.

Expert Reply
Sat May 28, 2011

In this type of problem, we must divide the object whose resistance we are calculating into concentric elements of infinitesimal thickness dr. We start by using the differential form of replacing r for the distance variable: , where dR is the resistance of the element of thicknessdr and surface area A.In this example, we take as our representative concentric elements a hollow cylinder of pipe of length L=1m.Any current passes from inner conductor to outer one must past radially through the concentric elements, and the area  through which the current passes as A=2L (This is the curved surface area -circumference multiplied by length of our hollow cylinder of thickness dr). Hence the required resistance is 
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