Engineering Determine Io and Vo in the circuit

[icesalmon]

Homework Statement

Determine io and vo

Relevant Equations

Ohms law: V=I*R

I am calling the voltage at the node the 2ohm resistor V_A
at Node A: ( V_A - 54 ) / 3 + ( V_A - V_o ) / 1 + (V_A - 0) / 2 = 0
at Node V_o: (V_o - V_A) / 1 - 2*i_o = (V_o - 54) / 2
i_o = V_A/2
at Node A: V_o - V_A)/1 - 2*(V_A/2) = (V_o - 54)/2
V_o = 4*V_A - 54
Node A: (V_A - 54)/3 + V_A - (4*V_A - 54) + V_A/2 = 0
V_A = 16.6V
V_o = 12.4V
i_o = 8.3A
The solution does not use Node Voltage, instead using a super mesh on the bottom two loops and solving that way which is fine. But it produces a value of V_A = 114V and i_o = 36A.

 

[berkeman]

Homework Statement:: Determine io and vo
Relevant Equations:: Ohms law: V=I*R

at Node Vo: (Vo - VA) / 1 - 2*io = (Vo - 54) / 2

This looks like a sign error in the RHS, and why did you use a different form of writing the sum of all currents out of a node is zero? It's best to stick with that form for each equation instead of trying to flip some of the currents, IMO.

 

[icesalmon]

This looks like a sign error in the RHS, and why did you use a different form of writing the sum of all currents out of a node is zero? It's best to stick with that form for each equation instead of trying to flip some of the currents, IMO.

Got it, good catch! Thanks! I'm not sure why I do that, my brain just flips between the two as I write the equations out. I wrote it as the sum of the currents being 0 and it worked out great, good tip!

 

[berkeman]

Glad that it helped. Did it resolve the discrepancy?

I've found that I need to stay single-minded (and simple-minded) in problems like this. If I try to get creative, it usually comes back to bite me in the end.

 

[icesalmon]

Glad that it helped. Did it resolve the discrepancy?

I've found that I need to stay single-minded (and simple-minded) in problems like this. If I try to get creative, it usually comes back to bite me in the end.

yeah, it yielded the answer from the solution!