Work, Energy, and Emf — Question 2

Question 2

Recharging requires terminal voltage above the opposing emf

A rechargeable cell has emf $\mathcal E=6.00$ V and internal resistance r=.200 ohm. An external charger forces 2.00 A into its positive terminal for 100 s. Assume reversible chemistry apart from the stated resistance.

1. Find the required cell terminal voltage and power entering the cell.

2. Separate the incoming energy into chemical storage and heat, and find charging efficiency.

Question 2 - Solution

Recharging requires terminal voltage above the opposing emf

(a) Method and calculation

$$V=\mathcal E+Ir=6.00+2(.200)=6.40\,\mathrm V.$$$$P_{\mathrm{in}}=VI=12.8\,\mathrm W.$$

(b) Interpretation and further calculation

$$W_{\mathrm{chem}}=\mathcal EIt=1200\,\mathrm J,\quad W_r=I^2rt=80.0\,\mathrm J.$$$$\eta_{\mathrm{charge}}=W_{\mathrm{chem}}/W_{\mathrm{in}}=1200/1280=.9375.$$

Physical check

Positive current entering the positive terminal makes the cell a net absorber of electrical energy.