Problem 2

A resistor

R

is connected to an ideal battery of emf

V

. Find the current and power. Assume ideal objects and components, neglect unstated losses, and use SI units. (a) Derive the primary requested quantity from the appropriate law. (b) Analyze quantitatively how the result depends on the given parameters. (c) Check a physically meaningful limiting case and explain its meaning. State sign conventions, show reasoning, and check dimensions. (a) Calculate the requested quantity from the data. (b) Give the law or expression showing parameter dependence. (c) Examine a limit consistent with the model. The source has emf E and internal resistance r; load R is in series, with terminal voltage U and current I.

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

\frac{dP}{dR}=\frac{\mathcal E^2(r-R)}{(R+r)^3}

problems.proof.analysis

A limiting case can expose a sign error or missing constraint; an implausible limit calls for checking the model and algebra.