hey i'm stumped with a question that deals with finding unknown node voltages as I only know how to complete part of the problem. here is the circuit, sorry for the crude MSPaint I do not have a working scanner here.

http://img7.imageshack.us/img7/8730/circuiti.png [Broken]

the answers are

v1 = 16.97V

v2 = 23.85V

v3 = 16.06V

I am stuck trying to figure out how these have been reached

First I tried KCL to get three equations on each of the three unknowns

v1

(v1-v3) / 20 + (v1 - v2) / 20 + v1 / 5 = 0

v2

(v2-v1) / 2 + (v2 - v3) / 5 - 5 = 0

v3

(v3 - v2) / 5 + (v3 - v1) / 20+ v3 / 10 = 0

I was told it is easy to put these together if it is imagined that the arbitrary current directions are thought to be leaving the node, except with v2 where the 5 amps are entering the node. apparently the answer will still be fine at the end of all of this.

at this point I have no clue how they manipulated these equations into finding the node voltages, what I keep reading is "use the equations to solve for node voltages" which means I'm missing something really obvious as they never bother to explain the process used to find the voltages. can someone please tell me what that is, I would really appreciate it as this is definitely the unit of study i need the most help with. thanks for reading.

http://img7.imageshack.us/img7/8730/circuiti.png [Broken]

the answers are

v1 = 16.97V

v2 = 23.85V

v3 = 16.06V

I am stuck trying to figure out how these have been reached

First I tried KCL to get three equations on each of the three unknowns

v1

(v1-v3) / 20 + (v1 - v2) / 20 + v1 / 5 = 0

v2

(v2-v1) / 2 + (v2 - v3) / 5 - 5 = 0

v3

(v3 - v2) / 5 + (v3 - v1) / 20+ v3 / 10 = 0

I was told it is easy to put these together if it is imagined that the arbitrary current directions are thought to be leaving the node, except with v2 where the 5 amps are entering the node. apparently the answer will still be fine at the end of all of this.

at this point I have no clue how they manipulated these equations into finding the node voltages, what I keep reading is "use the equations to solve for node voltages" which means I'm missing something really obvious as they never bother to explain the process used to find the voltages. can someone please tell me what that is, I would really appreciate it as this is definitely the unit of study i need the most help with. thanks for reading.

**1. Homework Statement****2. Homework Equations****3. The Attempt at a Solution**
Last edited by a moderator: