Problem 2

An ideal source of emf

\mathcal E

and internal resistance

r>0

is connected to a variable resistive load

R>0

. In steady state the circuit current is

I=\mathcal E/(R+r)

, and the load power is the electrical energy delivered to

R

per unit time. Ignore temperature changes and any other circuit elements. (a) Express the load power in terms of

R

. (b) Determine the load resistance that maximizes that power. (c) Find the maximum power and compare it with the source emf and internal resistance.

problems.proof.stepOf

P=I^2R=\mathcal E^2R/(R+r)^2

problems.proof.analysis

First identify the physical model and convention that match the stated setup. This fixes the signs used in the equations that follow.