Node-Voltage Method for Calculating Power Delivered by Dependent Voltage Source

[orangeincup]

Homework Statement

Use the node-voltage method to calculate the power delivered by the dependent voltage source.

Homework Equations

i1+i2+..in=0(KCL)
i=v/R
p=i*v

The Attempt at a Solution

I posted the solution below, but I'm going to post my own workings, based on just the circuit. I'm confused how they got their answer in the solution.

My workings:

v0-160/10Ω+i0/100Ω+150i0/50=0

I can reduce it to say i0*x=v0*x but I don't see how I could solve for either.

In their solution,they have (v0-150i0)/50 for the last part. Wouldn't it not be v0, since it's a different source?

Also, I have two unknowns, why did they only use one equation? I'm unsure of when I have to use one or two or more equations for node voltage questions. In this question, I felt like I would need two equations to solve it, but their solution only has one.

 

[ehild]

Homework Statement

Use the node-voltage method to calculate the power delivered by the dependent voltage source.

Homework Equations

i1+i2+..in=0(KCL)
i=v/R
p=i*v

The Attempt at a Solution

My workings:

v0-160/10Ω+i0/100Ω+150i0/50=0

The equation is wrong. You miss parentheses. You need to have sum of currents, but what is i0/100Ω? In the middle branch, you have iσ current. The dependent voltage source has emf=150 iσ. The current in the branch on the right the current is io, not the same as iσ. io flows through the potential difference V0-150 iσ.


ehild

 

[orangeincup]

The equation is wrong. You miss parentheses. You need to have sum of currents, but what is i0/100Ω? In the middle branch, you have iσ current. The dependent voltage source has emf=150 iσ. The current in the branch on the right the current is io, not the same as iσ. io flows through the potential difference V0-150 iσ.


ehild

Okay, I understand it better since I last posted. My equation now is the same as the solution,

(v0-160)/10 + v0/100 + (v0-150iσ)/50=0

Once I reduce it to iσ=(-v0/100), how do you solve for iσ or v0? I have only one equation and two unknowns.

 

[ehild]

Substitute iσ=(-v0/100) into the first equation. One unknown remains: v0. Solve for v0, use the value to get iσ=(-v0/100).

ehild

 

[orangeincup]

Where does iσ=(-v0/100) come from? Is it because of the middle?

 

[ehild]

The downward current on the middle branch is v0/100. The upward current is denoted by iσ.

ehild

 

[Brandon Sayareh]

https://www.google.com/url?q=https:...lendar&usd=2&usg=AOvVaw2WxIK5PKi4HEh2-ybhO_GN