Work, Energy, and Emf — Question 7

Question 7

Two opposing sources exchange energy through the same current

In a steady loop, a 20.0 V ideal source delivers current I=2.00 A, while a 12.0 V ideal rechargeable source is traversed from positive to negative internally. All resistance is external.

1. Find the rates of chemical energy release and storage.

2. Find total resistor heating and the total resistance required by the energy balance.

Question 7 - Solution

Two opposing sources exchange energy through the same current

(a) Method and calculation

$$P_{20}=20.0(2.00)=40.0\,\mathrm W\quad\text{released}.$$$$P_{12}=12.0(2.00)=24.0\,\mathrm W\quad\text{stored}.$$

(b) Interpretation and further calculation

$$P_R=40.0-24.0=16.0\,\mathrm W.$$$$R_{\mathrm{total}}=P_R/I^2=16.0/4.00=4.00\,\Omega.$$

Physical check

The smaller source absorbs energy because current enters its positive terminal; the word source does not guarantee positive delivered power.