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

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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.
 
Attachments
  • Circuit schematic with a 7V source on the left, a 6V source in the middle-left branch, and resistors of 1 ohm, 2 ohms, 3 ohms, 2 ohms and 1 ohm, with nodes labelled A, B, C, D and current I at the top.
    Circuit Diagram 2.jpg
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Discussion

-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.