Question

Consider a material of resistivity $\rho$ in a shape of a truncated cone of altitude h and radii a & b for the right and the left ends respectively as shown in figure. The resistance between the two end is:

• A. $\frac{\rho h}{2\pi ab}$
• B. $\frac{\rho h}{\pi (a^2+b^2)}$
• C. $\frac{\rho h}{\pi ab}$
• D. $\frac{2\rho h}{\pi ab}$

Answer 1

The correct option is C $\frac{\rho h}{\pi ab}$

We know that

$R=\frac{\rho L}{A}$

Given,

$\rho =pl=h$

Area can be calculated as,

$A=\sqrt{A_1{A}_2}=\sqrt{\pi a^2\pi b^2}=\pi \sqrt{a^2{b}^2}$

$=\pi ab$

Now resistance between two end is

$R=\frac{\rho h}{\pi ab}$

Option (C) is correct option