Network Analysis Techniques

DC Mesh Current Analysis

8 questions By Tony R. Kuphaldt

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Question 4 of 8

Write two KVL loop equations for this circuit, using I₁ and I₂ as the only variables:

Reveal answer

KVL equation for left-hand loop:

6 − 1000I₁ − 1000(I₁ I₂) 1 = 0

KVL equation for right-hand loop:

7.2 − 1000I₂ − 1000(I₁ I₂) 1 = 0

Follow-up question: what are the values of I₁ and I₂, based on this system of equations?

Notes:
Students’ equations may not look exactly like these, depending on how they “stepped” around the loops tallying voltage drops. So long as they are all able to reach the same answers for I₁ and I₂, it does not matter. In fact, it is a good thing to have different students propose different forms of the equations to demonstrate that the same answers are obtained every time.
Question 5 of 8

Describe, step-by-step, the steps required to calculate all currents and voltage drops in a DC network using the Mesh Current Method.

Reveal answer

There are several textbooks and other references delineating the steps required in this analysis method. I leave the task of researching these steps to you!

Notes:
Students may find slight differences between variations of the “Branch Current” method of analysis described in different references. However, these differences are of no consequence.
Question 6 of 8

Write the KVL equations for this circuit, given the following mesh current directions, and then solve for the charging current through battery #1:

Now, write the KVL equations for the same circuit, after reversing the direction of mesh current I₂. How does this reversal of mesh current I₂ affect the writing of the two KVL equations, and also the calculation of the answer for battery #1’s charging current?

Reveal answer

KVL equations with currents I₁ and I₂ meshing with each other through battery #1:

0.5I₁ + 0.2I₁+ 0.2(I₁+ I₂) + 1.5(I₁ + I₂) + 23.5 − 29 = 0

1.5(I₁ + I₂) + 0.2(I₁ + I₂) + 0.2I₂ + I₂ − 24.1 + 23.5 = 0

KVL equations with currents I₁ and I₂ meshing against each other through battery #1:

0.5I₁ + 0.2I₁+ 0.2(I₁ − I₂) + 1.5(I₁ − I₂) + 23.5 − 29 = 0

1.5(I₂ − I₁) + 0.2(I₂ − I₁) + 0.2I₂ + I₂+ 24.1 − 23.5 = 0

I_bat1 = 1.7248 A

Notes:
Your students may find the setup of KVL equations easier with the two mesh currents going in the same direction through battery #1, but they should be able to arrive at the same answer either way. It is very important to your students’ understanding of the Mesh Current technique that they are able to handle both situations!