Other Single-Loop Circuits — Question 1

Question 1

An opposing source can reverse the assumed loop current

Two ideal sources of 8.00 V and 12.0 V have their positive terminals connected through a 4.00 ohm resistor. Their negative terminals are joined by ideal wire. Define I clockwise as drawn, leaving the positive terminal of the 8.00 V source.

1. Find the signed current and actual direction.

2. Find power delivered or absorbed by each source and resistor heating.

Question 1 - Solution

An opposing source can reverse the assumed loop current

(a) Method and calculation

$$8.00-12.0-4.00I=0.$$$$I=-1.00\,\mathrm A\quad\text{(actual current counterclockwise)}.$$

(b) Interpretation and further calculation

$$P_{8,\mathrm{delivered}}=8I=-8.00\,\mathrm W,\quad P_{12,\mathrm{delivered}}=-12I=12.0\,\mathrm W.$$$$P_R=I^2R=4.00\,\mathrm W=12.0-8.00.$$

Physical check

The 8 V source absorbs 8 W; its positive emf does not force it to deliver power.