Multiloop Circuits — Question 7

Question 7

A voltage source between unknown nodes creates a supernode constraint

Nodes A and B connect to ground through 2.00 ohm and 3.00 ohm respectively. An ideal 5.00 V source connects A to B with B positive. An external current driver injects 3.00 A into A and returns through ground.

1. Use a combined-node current equation and the voltage constraint to find VA and VB.

2. Find the current through the 5.00 V source from A to B and its delivered power.

Question 7 - Solution

A voltage source between unknown nodes creates a supernode constraint

(a) Method and calculation

$$V_A/2+V_B/3=3,\quad V_B-V_A=5.$$$$3V_A+2(V_A+5)=18\Rightarrow V_A=1.60\,\mathrm V,\quad V_B=6.60\,\mathrm V.$$

(b) Interpretation and further calculation

$$I_{AB}=V_B/3=2.20\,\mathrm A=3-V_A/2.$$$$P_{5}=5I_{AB}=11.0\,\mathrm W\quad\text{delivered}.$$

Physical check

The unknown current through an ideal voltage source is found from a node balance after the potentials are solved.