Mesh Analysis: Solve I, Vab, Vac, Vbd, Vcd

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SUMMARY

The discussion focuses on solving a circuit using the Mesh Analysis method to determine the currents (I1, I2, I3) and voltages (Vab, Vac, Vbd, Vcd). The original equations presented by the user contained errors in voltage polarity and missing terms. The corrected approach involves setting up three equations based on the mesh currents and applying Kirchhoff's Voltage Law (KVL) to derive the relationships between the currents and voltages. The final expression for Vab is derived from the voltage drop across a 1-ohm resistor, calculated as Va - Vb = (I1 - I2) * 1 ohm.

PREREQUISITES
  • Understanding of Mesh Analysis in electrical circuits
  • Familiarity with Kirchhoff's Voltage Law (KVL)
  • Basic knowledge of circuit components such as resistors and voltage sources
  • Ability to solve systems of linear equations
NEXT STEPS
  • Study advanced Mesh Analysis techniques for complex circuits
  • Learn how to apply Kirchhoff's Laws in circuit analysis
  • Explore methods for solving systems of equations in electrical engineering
  • Investigate voltage drop calculations across various resistor configurations
USEFUL FOR

Electrical engineering students, circuit designers, and anyone involved in analyzing and solving electrical circuits using Mesh Analysis.

Kobayashi
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Homework Statement


For the following circuit determine:
I, Vab, Vac, Vbd, Vcd

See attachment for circuit diagram.


Homework Equations


Mesh Analysis method



The Attempt at a Solution


Using mesh analysis:

-7V + I1 - I2 + 6V + 2I1 -2I3
= 3I1 - I2 -2I3 ------------------mesh 1

2I2 + 3I2 -3I3 + I2 - I1
= -I1 + 6I2 -3I3 -----------------mesh2

I3 + 2I3 -2I1 -6 + 3I3 - 3I2
= -2I1 - 3I2 + 6I3 -6 -------------mesh 3

Have I done this correctly? How do you get I from this and the voltages?

Thanks.
 

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  • Circuit Diagram 2.jpg
    Circuit Diagram 2.jpg
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-7V + I1 - I2 + 6V + 2I1 -2I3
= 3I1 - I2 -2I3 ------------------mesh 1
The right hand side is missing the voltage. The sum of the voltages around each loop = 0.

The polarity convention is reversed. I would have done it:

7V - I1 + I2 - 6V - 2I1 + 2I3 = 0, for mesh 1.

So, 7V - 3I1 + I2 + 2I3 = 0, and likewise with the others. One then has 3 equations and 3 unkowns (I1, I2, I3), for which one can solve. Simply add the equations together and eliminate all but one current so that currents are found in terms of voltage and resistance.

Then Vab is just the voltage drop across the resistor (1 ohm) or Va - (I1-I2) 1 ohm = Vb or Va - Vb = (I1 - I2) * 1 ohm.
 

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