Q 19. Find the resistance of an ellipse with major axis \(a\), and minor axis \(b\), rotated about its major axis, with the parts beyond \(\pm c\) being cut off as shown in diagram. Its resistivity is \(\rho\).

Answer:

By setting up the integral and integrating, we get

\[R = \frac{\rho a}{\pi b^2} \ln \left| \frac{a+c}{a-c} \right|\]

This expression is valid for all \(c < a\).

For a similarly cut sphere(\(a=b\)),

\[R = \frac{\rho}{\pi a} \ln \left| \frac{a+c}{a-c} \right|\]