Find voltage using nodal analysis

[Martin V.]

Homework Statement

Assignment: Find V_2 using Nodal Analysis

Homework Equations

KCL
U=R*I

The Attempt at a Solution

- Chosen reference node
- Assigned node voltages
- Applied KCL to each non-reference node
- Solve system of equation
- Checked equations for obvious errors

See circuit drawing, node labels and assumed current direction in Nodal.png. Equation and solution of equation is to find in Nodal 2.png.

The right result should be that V_2=13,84V and not V_1 as I get.

 

[CWatters]

Not sure if this is the only mistake but KCL at node 2 is wrong...

Personally I prefer to write for my KCL equations to sum to zero so I would write...

Assume current leaving a node is +ve then..

+ I₄ + I₅ = 0
and
I₄ = -I₅

You might be tempted to skip steps but you have to be very fussy about the signs when applying KCL or KVL. I find I make fewer mistakes if I write my equation so it sums to zero and don't take shortcuts.

 

[CWatters]

Your working for KCL at node 1 looks correct but I would write..

Assume current leaving the node is +ve..

-I₁ + I₂ +I₃ = 0

Then rearrange it. It may seem fussy but by sticking to this version of the KCL definition I find I make few mistakes.

 

[Martin V.]

Both KCL-equations is wrong. With #2 is found the error in the equation around node 2. For node 1 were the 10 V battery not included in the equation. With the two change I get the correct answar - thanks! :)

 

[theodoros.mihos]

I agree with Martin V. I found $V_1\approx10.2426...(V)$ and $V_2\approx13.9012...(V)$.