Help with nodal analysis question
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Help with nodal analysis question

[From: ] [author: ] [Date: 12-02-14] [Hit: ]
you can help.CKT: http://i42.tinypic.com/iy067m.My attempt: http://i40.tinypic.......
Please, I need help on this question. I feel like I'm on the brink of solving this and need some help with the rest, or If I messed up somewhere, you can help.

CKT: http://i42.tinypic.com/iy067m.jpg

My attempt: http://i40.tinypic.com/2qmm2s5.jpg

Question: Solve the following circuit for the value of the current through the 5K ohm resistor using nodal analysis.Also I can't use source conversion.

Please help, I really need help on this

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Start off with a KCL node equation @ node Va: (currents leaving = positive and currents entering = negative)

At node Va, I have a current entering from the left, and currents leaving down and right of the node. so you get:

[ 10 - Va ] / 2k = Va / 1k + [ Va - Vb ] / 4k

expand terms:

10 / (2k) - Va / (2k) = Va / (1k) + Va / (4k) - Vb / (4k)

factoring the terms we get equation 1:

Va * (-7 / 4k) + Vb * (1 / 4k) + 10/2k = 0

KCL @ Vb node: (currents leaving = positive and currents entering = negative)

At this node, I have a current entering from the left, and currents leaving down and right.

[ Vb - 6 ] / [ 1k + 2k ] + Vb / (5K) = [ Va - Vb ] / (4k) ----> remember the 1k and 2k add

expand terms:

Vb / (3k) - 6 / (3k) + Vb / (5k) = Va / (4k) - Vb / (4k)

factoring each Va and Vb term we get:

Va * [ -1 / (4k) ] + Vb * [ 47 / (60k) ] - 6 / (3k) = 0

Now this is a simple linear equation with 2 equations + 2 unknowns. using any method you want, you get:

Va = 3.3757 V

and:

Vb = 3.6305 V

Now the current through the 5k resistor is:

I = Vb / (5k) = 3.6305 / (5k) = 0.7261 mA
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