Explaining Mesh Currents: Understanding the Relationship between i1 and i2

[rugerts]

Homework Statement

Find the power developed by the dependent voltage source

Relevant Equations

KVL, KCL

Here's my work.

I have the correct answer, but I'd like to know why this only works for (i1-i2) plugged in for i_delta as opposed to what I initially put: i_delta = i2-i1. You can see this in the blue text above versus what I originally had in red.

 

[collinsmark]

I have the correct answer, but I'd like to know why this only works for (i1-i2) plugged in for i_delta as opposed to what I initially put: i_delta = i2-i1. You can see this in the blue text above versus what I originally had in red.

Each of the following currents (as they are defined), $i_1, i_2,$ and $i_\Delta$ pass through the $20 \ \Omega$ resistor.

Looking only at a particular current as it passes through the $20 \ \Omega$ resistor,

Is $i_1$ in the same direction as $i_\Delta$, or is it in the opposite direction?

Is $i_2$ in the same direction as $i_\Delta$, or is it in the opposite direction?

Given that, how must you define $i_\Delta$ in terms of $i_1$ and $i_2$?

 

[rugerts]

Each of the following currents (as they are defined), $i_1, i_2,$ and $i_\Delta$ pass through the $20 \ \Omega$ resistor.

Looking only at a particular current as it passes through the $20 \ \Omega$ resistor,

Is $i_1$ in the same direction as $i_\Delta$, or is it in the opposite direction?

Is $i_2$ in the same direction as $i_\Delta$, or is it in the opposite direction?

Given that, how must you define $i_\Delta$ in terms of $i_1$ and $i_2$?

Oh... I see now. Basically i_delta's defined direction gives it all away. Thanks for the reply