# I can only find 3 of the 4 equations to satisfy 4 unknowns. What am I missing?

#### thatsmessedup

Joined Feb 15, 2018
28
I cant seem to find the last equation to solve for this kvl. Where is the last equation hiding?

#### MrAl

Joined Jun 17, 2014
6,810
Hi,

It looks like you have four nodes there so why not four equations?
Did you write for each node?

#### WBahn

Joined Mar 31, 2012
24,974
It would help if you used your colors consistently. In your second diagram you have two yellow nodes and the pink node from the first diagram has disappeared.

Also, in your first diagram your dependent current source is controlled by "Vs", but there is no "Vs" identified on the diagram.

Then, in your second diagram, it is controlled by "Vb", so why the switch?

If you are counting "Vb" in the second diagram as an unknown, the what is the relationship between Vb, I1, and your R123 equivalent resistor?

EDIT: Fixed typo pointed out below by The Electrician. Thanks!

Last edited:

#### The Electrician

Joined Oct 9, 2007
2,751
All you need is the two mesh currents you've labeled A and B (which are the same as i1 and i2). Two equations suffice to find those two Everything else falls out from them.

#### thatsmessedup

Joined Feb 15, 2018
28
I don't follow. What specifically will get me the last equation I need to solve this?

#### WBahn

Joined Mar 31, 2012
24,974
I don't follow. What specifically will get me the last equation I need to solve this?
At the risk of repeating myself... what is the relationship between Vb, I1, and your R123 equivalent resistor?

EDIT: Fixed typo pointed out below by The Electrician. Thanks!

Last edited:

#### thatsmessedup

Joined Feb 15, 2018
28
At the risk of repeating myself... what is the relationship between Vb, I2, and your R123 equivalent resistor?
I see where you are getting at. using OHMs law for Vb, R123 and I1 we can get another independent equation.
Thanks.

#### The Electrician

Joined Oct 9, 2007
2,751
At the risk of repeating myself... what is the relationship between Vb, I2, and your R123 equivalent resistor?
Don't you mean "what is the relationship between Vb,I1, and your R123 equivalent?"
The TS seems to have picked up on that.

#### The Electrician

Joined Oct 9, 2007
2,751
I don't follow. What specifically will get me the last equation I need to solve this?
What you've done is almost a solution by branch currents. Do you know the supermesh technique?

#### WBahn

Joined Mar 31, 2012
24,974
Don't you mean "what is the relationship between Vb,I1, and your R123 equivalent?"
The TS seems to have picked up on that.
Yep. Thanks for pointing out the typo. I'll fix it.

#### WBahn

Joined Mar 31, 2012
24,974
What you've done is almost a solution by branch currents. Do you know the supermesh technique?
My impression is that they are just covering KCL/KCL and applying them to branches and loops. My guess is that they'll be hitting mesh and nodal analysis pretty soon, depending on when they cover superposition.