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

problems.proof.prevStep problems.proof.nextStep

dP/dR=\mathcal E^2(r-R)/(R+r)^3

problems.proof.analysis

This equation expresses the physical law governing the system. It incorporates the stated constraint rather than treating the relevant quantities as independent.

problems.proof.pitfall. Check the sign convention and physical case carefully; do not use a formula for a different motion or geometry.