Problem 2
A DC source of emf E and internal resistance r supplies a purely resistive load R in series; take E and r as constant and the leads ideal. The circuit reaches steady current, the terminal voltage is U, and useful power is delivered to the load. (a) Express current and load voltage in terms of R. (b) Find the load R for maximum power and that maximum. (c) Find efficiency there, defined as load power divided by the power supplied by the ideal emf. Use SI units throughout and treat components as ideal exactly as specified. State sign conventions when writing equations and retain units in final results.
problems.proof.stepOf
problems.proof.analysis
The equation follows by applying the physical law to the chosen system; ideal constraints link the variables. Signs must remain consistent with the defined directions.
problems.proof.pitfall. Pitfall: do not change sign conventions between equations; a negative sign may encode direction rather than an invalid result.