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## Homework Statement

Given the following circuit using mesh's method to solve for the power of the dependent source.

Using the same circuit and using the node voltage method solve for the power of the dependent source.

Circuit:

## Homework Equations

Noting that I have to implement a super mesh for the dependent source to solve the unknown currents. I have arrived to the following equations

[itex]Vx = 4I_1[/itex]

[itex]3Vx = I_2 - I_1[/itex]

The Mesh equation:

[itex]-4I_1-12I_2+30-8I_1-20 = 0[/itex]

Simplifying:

[itex]-12I_1-12I_2+10 = 0[/itex]

## The Attempt at a Solution

Solving the simulatenous equations by doing various substitutions of

[itex]Vx = 4I_1[/itex]

[itex]3Vx = I_2 - I_1[/itex]

By solving the mesh equations for [itex]I_1 = \frac{10}{12} - I_2[/itex]

I have arrived at the following solutions

[itex]I_1 = \frac{5}{84}[/itex]

[itex]I_2 = \frac{65}{84}[/itex]

[itex]Vx = \frac{5}{21}[/itex]

[itex]3Vx = \frac{5}{7}[/itex]

Checking by Kirchoff's voltage law to see if all voltages within the outter loop it does equate to 0.

I need a check to see if this is right and I have no idea how to properly implement the node voltage method because the equations do not seem to come out right. I think my trouble is properly putting the correct polarity/sign convention of all devices

Help! Thanks!

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