A tapered bar of length L and end diameters D | vedclass

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(D) The resistance $R$ of a conductor of length $L$,resistivity $\rho$,and cross-sectional area $A$ is given by $R = \frac{\rho L}{A}$.For a tapered b

Vedclass · Accepted Answer

$\frac{4 \rho L}{\pi D_1 D_2}$

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(D) The resistance $R$ of a conductor of length $L$,resistivity $\rho$,and cross-sectional area $A$ is given by $R = \frac{\rho L}{A}$.For a tapered bar (frustum of a cone),the effective cross-sectional area $A$ is the geometric mean of the areas of the two ends.The area of the ends are $A_1 = \frac{\pi}{4} D_1^2$ and $A_2 = \frac{\pi}{4} D_2^2$.The effective area is $A = \sqrt{A_1 A_2} = \sqrt{\left(\frac{\pi}{4} D_1^2\right) \left(\frac{\pi}{4} D_2^2\right)} = \frac{\pi}{4} D_1 D_2$.Substituting this into the resistance formula:$R = \frac{\rho L}{\frac{\pi}{4} D_1 D_2} = \frac{4 \rho L}{\pi D_1 D_2}$.

$A$ tapered bar of length $L$ and end diameters $D_1$ and $D_2$ is made of a material of electrical resistivity $\rho$. The electrical resistance of the bar is

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