Why are there no solutions to this Single Loop Circuit exercise?

[BlackOps]

Here is an exercise from the book Engineering Circuit Analysis, by Hayt&Kemmerly.

**broken link removed**

Find v3 if:
a) the 90v source generates 180W
b) the 90v source adsorbs 180W
c) the dependent source generates 100W
d) the dependent source adsorbs 100W

i began to do it like that:

P = IV, => 180 = 90i, i = 2A.

-20v + 10i + 90v + v3 = 0
v3 = -90v

but...then i looked at the answers at the back of the book, and the answer was:
(a-d) No Solution!

can anyone explain, why there is no solution??

 

[field_catcher]

Re: Single Loop Circuit

From KCL, the current going through R1 and R2 should be the same.

But by looking at the schematic, you will find ( by setting current flows from left to right) :

R1 current = v3 / 10

R2 current = -(1.8-1)v3/ 40

so unless v3=0, otherwise there is no solution to this problem.

 

[BlackOps]

Re: Single Loop Circuit

No!

One engineer helped me with explanation, and here is how it looks like:

in all the cases the following relations must hold:
-1.8V3 + 40i + V3 = 0, i = 0.02V3, if the dependent voltage source is supplying power(if the 90 V source supplies power then the current direction is such that the dependent voltage source must also supply power)

-1.8V3 - 40i + V3 = 0, i = -0.02V3, if the dependent voltage source is absorbing power.

a) Well, in the first case the 90V source is supplying the power so the
current is going out the positive terminal....so:

-90V + 10i + 20V - V3 = 0
i = (70V + V3)/10, and from above i = 0.02V3, so:

(70V + V3)/10 = 0.02V3
V3 = -87.5V
i = -87.5 * 0.02 = -1.75A

P = IV = -87.5 * (-1.75) = 153.125W, But the problem said that P = 180W, so "a" has No Solution

"b" is similiar.

c) The dependent source generages 100 W....so from the first equation , i = 0.02V3, and P = IV. so: 100W = 0.02V3*V3, V3 = sqrt(100/0.02) = 70.71v

i = 0.02 * 70.71v = 1.414A

The 90 V supply must also supply power by virtue of the current direction
so from part a:

i = (V3 + 70)/10 = (70.71 + 70)/10 = 14.071A

But 14.071A is not equal to 1.414A, so... "c" has no Solution

similiar with "d"

that was an explanation.

thanks all!