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

P_{max}=\mathcal E^2/(4r)

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Finally substitute the given values and check units and limiting behavior. The result agrees with the signs and scale implied by the model and previous parts.