Physic Labs

Problem 2

A source of emf ℰ and internal resistance r drives a resistor R. Find the current, power in R, and R maximizing that power. Use the stated ideal model: quantities are constant or vary only as specified, with no extra drag, losses, or external influences. State a sign convention, keep units consistent, and use a classical approximation only where appropriate. (a) Set up the governing equation from a fundamental law. (b) Solve for the requested quantity under the stated conditions. (c) Check the result using a suitable limit, sign, or unit test, and report both the expression and its physical meaning.I is the circuit current and P_R is the power dissipated in the load R.
dPR/dR=E2(r−R)/(R+r)3dP_R/dR=\mathcal E^2(r-R)/(R+r)^3
problems.proof.analysis

Solve the relation for the unknown while preserving algebraic signs and physical restrictions. Use any stated geometry or definition to express the result in the given data.