Problem 2

An ideal emf source

\mathcal E

in series with internal resistance

r

supplies a resistive load

R

; all components and wires remain at fixed temperature and the circuit is in steady state. (a) Find the current, source terminal voltage, and load power. (b) Find the value of

R

for maximum load power and that maximum. (c) At the maximum-power condition, compare power delivered by the source with power dissipated internally and state the load-power efficiency.

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

P_R=I^2R=\frac{\mathcal E^2R}{(R+r)^2}

problems.proof.analysis

The load's Joule power is $I^2R$ . Substituting the circuit current expresses it as a function of $R$ for optimization.