Work, Energy, and Emf — Question 5

Question 5

Loaded terminal measurements identify emf and internal resistance

A source delivers terminal voltage 11.6 V at current 1.00 A and 10.4 V at current 4.00 A. Assume $V=\mathcal E-Ir$ with constant positive r.

1. Infer emf and internal resistance.

2. Find terminal power and internal power at 4.00 A, and the fraction of chemical power delivered externally.

Question 5 - Solution

Loaded terminal measurements identify emf and internal resistance

(a) Method and calculation

$$r=\frac{11.6-10.4}{4.00-1.00}=.400\,\Omega.$$$$\mathcal E=V+Ir=11.6+.400=12.0\,\mathrm V.$$

(b) Interpretation and further calculation

$$P_{\mathrm{out}}=(10.4)(4)=41.6\,\mathrm W,\quad P_r=4^2(.400)=6.40\,\mathrm W.$$$$\eta=41.6/(12\cdot4)=.866667.$$

Physical check

The intercept is emf and the negative slope is internal resistance; terminal voltage alone does not identify either.