Problem #0268 Electricity & Magnetism Sub-menu Problem #0270 Chapters Chapters

539.

Problem 39.29 (RHK)

We have to show that in the circuit shown in the figure the power dissipated in the resistance R is maximum when , in which r is the internal resistance of the AC generator.

Solution:             Click For PDF Version

Let the emf of the AC-generator be

.

As the total resistance in the resistance in the circuit is , the current in the circuit will be

The average power dissipated in the circuit will be

The function will have an extremum at R for which

This condition gives

By calculating , we will show that it is <0, and therefore is a maximum.

The power dissipation is maximum when the external load is equal to the load of the generator.