Calculate the power consumed by dependent source

[ongxom]

Homework Statement

calculate the power consumed by dependent source

Homework Equations

The Attempt at a Solution

The 10A source does not build a supermesh.
Loop 3:
(i₃-i₂).(1/10)=0 => i₃=i₂
Loop 2 :
i₂=10(A)
i₃=10(A)
v_x.(10)=10=> v_x=1(V) (node voltage)
also for loop 2 :
1/10(i2-i3)-3vx+(1/110)(i2-i1)=0
i₁=-320(A)
To calculate the power consumed p=v.i=-3v_x.i

I am not sure what current goes through the dependent source, i think it is (i₂-i₁)

 

[mfb]

Is there something missing on the left side? A power supply?

(i₃-i₂).(1/10)=0

Why should this be zero?

v_x.(10)=10

Where does that come from?

I am not sure what current goes through the dependent source, i think it is (i₂-i₁)

Right.

 

[ongxom]

Is there something missing on the left side? A power supply?

Why should this be zero?
Where does that come from?
Right.

1) Nothing is missing.
2) Maybe no voltage source was on the left side.
3) Fix it, it should be vx.(1/(1/10))=-10 (cause the 10A source is going out the node).
Is the equation for Loop 2 correct ?

 

[gneill]

If there is nothing missing on the left then there is no loop 3, and no i₃. Furthermore, the 10A source will fix the mesh current i₂ at 10A (because the 10A source is in a portion of that mesh that is not shared with any other mesh and so that mesh current is the only current that flows in that branch making the mesh current identical to the current in that branch).

So you've got a value for mesh current i₂ by inspection, and only have i₁ to solve. Given that you know i₂, what's Vx? Can you write KVL for the i₁ mesh?

 

[ongxom]

If there is nothing missing on the left then there is no loop 3, and no i₃. Furthermore, the 10A source will fix the mesh current i₂ at 10A (because the 10A source is in a portion of that mesh that is not shared with any other mesh and so that mesh current is the only current that flows in that branch making the mesh current identical to the current in that branch).

So you've got a value for mesh current i₂ by inspection, and only have i₁ to solve. Given that you know i₂, what's Vx? Can you write KVL for the i₁ mesh?

v_x=-1 (V)
KVL for mesh 1 :
(1/110).(i₁-i₂)+3v_x+(1/100).i₁=0

 

[gneill]

v_x=-1 (V)
KVL for mesh 1 :
(1/110).(i₁-i₂)+3v_x+(1/100).i₁=0

Yes, that looks good. So what's i₁? How about the net current flowing into the dependent source?

 

[ongxom]

Yes, that looks good. So what's i₁? How about the net current flowing into the dependent source?

substitute v_x=-1, i₂=10A we have i₁=161.9(A).
p=-3v_x.(i₂-i₁)=-3.(-1).(10-161.9)=-455.7(W)
Is the result correct now ?

So according to the diagram, i₃ should be eliminated and the above equation of mine for mesh 2 was incorrect, right ?

 

[gneill]

substitute v_x=-1, i₂=10A we have i₁=161.9(A).
p=-3v_x.(i₂-i₁)=-3.(-1).(10-161.9)=-455.7(W)
Is the result correct now ?

The number 455.7 W is good. One thing to verify is whether or not the source is actually producing or consuming power. Suppose you label the device with the actual potential across it. Is the current entering or leaving via the more positive terminal? A voltage supply that is producing power has current leaving via its + terminal.

So according to the diagram, i₃ should be eliminated and the above equation of mine for mesh 2 was incorrect, right ?

Right.