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.
I=E/(2r),PR,max⁡=E2/(4r)I=\mathcal E/(2r),\quad P_{R,\max}=\mathcal E^2/(4r)
problems.proof.analysis

Check with an independent law, limiting case, or physical sign. This can expose a convention error and confirms that the linked parts use consistent data.