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.

 

[piercas]

I would say that your attempt at using mesh analysis looks correct. To find the values for I, Vab, Vac, Vbd, and Vcd, you can use the equations you have written and solve for each variable. For example, to find I, you can set up a system of equations using the equations for mesh 1, 2, and 3 and solve for I. Similarly, you can solve for Vab, Vac, Vbd, and Vcd by using the equations and known values in the circuit. Remember to use the correct signs for each variable (e.g. positive for clockwise currents and negative for counterclockwise currents) and always check your answers to make sure they make sense in the context of the circuit. Good luck with your homework!