# Mesh Analysis - confusion on writing equations

I'm quite confused by mesh analysis. I understand that the idea is basically to apply KVL to each mesh. For example, if you have a loop that contains, say, a 3ohm and 2ohm resistor, and that's it, what is the correct KVL equation? Is it simply 0=3I+2I?

At the bottom, I can understand the first equation: you have a 9V source, and the resistors must cause a 9V voltage drop. But the second equation, I don't understand. Why is the first term positive?

Last edited:

berkeman
Mentor
On your first question, yes, you would write 0=3I+2I. And you would solve it and get I=0, because there are no sources in your example.

In the second loop, the first term is positive because of the +/- sign convention on that resistor. In the first loop, the voltage across that resistor is a *voltage drop* following the direction of the first loop current as shown. But it is a *voltage gain* in the direction of the second current loop as shown. Make sense?

You just have to be careful and consistent in KVL loops to write drops as - voltage changes, and gains as + voltage changes.

Loop2: 0 = 3000(I1 - I2) - 2000I2 - 2000I2
yes it has to do with the passive sign convention. This equation can also
be written as follows
0 = -3000(I2 - I1) - 2000I2 - 2000I2.
I2 and I1 goes through 3Kohms, but in opposite directions. in the second loop just follow I2 and write the equation i wrote :) this avoids confusion
cheers