Problem #0137 Electricity & Magnetism Sub-menu Problem #0139 Chapters Chapters

408.

Problem 33.26 (RHK)

In the circuit shown in the figure , , and have constant values but R can be varied. We have to find an expression for R that results in the maximum heating in that resistor.

Solution:             Click For PDF Version

We will find the current flowing through R. We have a multi-loop circuit with one junction. Equations that follow from Kirchoff’s laws are

Also,

Rate of Joule heating in the resistance R is

We find the extremum solution of by requiring

This condition gives the equation

As

we have