# Mesh Analysis Problem

1. Nov 13, 2007

### Kobayashi

1. The problem statement, all variables and given/known data
For the following circuit determine:
I, Vab, Vac, Vbd, Vcd

See attachment for circuit diagram.

2. Relevant equations
Mesh Analysis method

3. 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.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

#### Attached Files:

• ###### Circuit Diagram 2.jpg
File size:
8.7 KB
Views:
63
2. Nov 14, 2007

### Staff: Mentor

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.