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

[Kobayashi]

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.

 

[Astronuc]

-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.