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Shown a conductor of length `l` having a circular cross section. The radius of cross section varies linearly form `a to b`. The resistivity of the material is`(rho)`.Assuming that `b-altltl`,find the resistance of the conductor. |
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Answer» Since radius of left end is a and that of right end is b, therefore increase in radius over length l is (b-a). Hence rate of increase of radius per unit length `=((b-a)/(l))` Increase in radius over length `x=((b-a)/(l))x` since radius at left end is a, radius at distance `x=r=a+((b-a)/(l))x` Area at this particualr section `A=pir^(2)=pi[a+((b-a)/(l))xx]^(2)` Hence curret density `J=(i)/(A)=(i)/(pir^(2))=(i)/(pi[a+(x(b-a))/(l)]^(2))` |
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