Work, Energy, and Emf — Question 8

Question 8

Energy measurements reconstruct hidden source parameters

During a 50.0 s discharge at constant current 2.00 A, a source releases 1500 J of chemical energy and delivers 1400 J to the load. Assume all missing energy heats a constant internal resistance.

1. Infer emf and internal resistance.

2. Find terminal voltage and verify it through both electrical and energy relations.

Question 8 - Solution

Energy measurements reconstruct hidden source parameters

(a) Method and calculation

$$Q=It=100\,\mathrm C,\quad\mathcal E=W_{\mathrm{chem}}/Q=15.0\,\mathrm V.$$$$r=\frac{W_{\mathrm{chem}}-W_{\mathrm{load}}}{I^2t}=100/200=.500\,\Omega.$$

(b) Interpretation and further calculation

$$V=\mathcal E-Ir=15.0-2(.500)=14.0\,\mathrm V.$$$$V=W_{\mathrm{load}}/Q=1400/100=14.0\,\mathrm V.$$

Physical check

Independent energy and terminal relations must agree if the internal-resistance model is adequate.