Answer to Question #276423 in Electric Circuits for Rex

Question

The insulation resistance of a kilometer of the cable having a diameter of 2 cm and an insulation thickness of 2 cm is 600 ohms. If the thickness of the insulation is increased to 3 cm, find the insulation resistance of the cable.

Answer 1

Explanations & Calculations

• The resistance can be thought proportional to the length and inversely to the area of the conductor according to the equation $\small R = \rho \large\frac{L}{A}$ .

$\qquad\qquad \begin{aligned} \small R &\propto\small \frac{L}{A}\\ \small 600 & =\small \frac{L}{\pi(4^2-2^2)}\cdots\cdots(1)\\ \small R&=\small \frac{L}{\pi(5^2-2^2)}\cdots\cdots(2)\\ \\ \small (2) \div(1),\\ \\ \small \frac{R}{600}&=\small \frac{(4^2-2^2)}{(5^2-2^2)} \end{aligned}$

• Initial total thickness is $\small 2+2=4\,cm$
• Final total thickness is $\small 2+3 = 5\,cm$
• The area of the resistive insulation is the difference between the (conductor+insulator) - (core).

• Now you can calculate the new resistance $\small R.$