Finding voltage on circuit, help

[Iyafrady]

I want to find the voltage V, the red pencil is what is given in the problem and the blue pencil is what i did.I labeled the voltage polarity across the resistors to follow the psc.I first did KCL on the right most node; (V/100)+(V/10)+(-V/25)+.2V=2.5, I solve for v and get V=9.26, but the answer in the book is V=50..dont know what I am doing wrong, the book and my prof. always say to follow the psc convention whenever possible, especially on passive elements like resistors!

 

[Defennder]

There's something unclear here. There's a 0.2V₁ dependent current source on the 2nd horizontal wire. But V₁ is marked nowhere on the diagram, so is it to be interpreted as V instead?

 

[Iyafrady]

oh yea sorry, .2V1 should be .2V

 

[Defennder]

I labeled the voltage polarity across the resistors to follow the psc.I first did KCL on the right most node; (V/100)+(V/10)+(-V/25)+.2V=2.5, I solve for v and get V=9.26, but the answer in the book is V=50..dont know what I am doing wrong, the book and my prof. always say to follow the psc convention whenever possible, especially on passive elements like resistors!

I'm guessing the reason why this doesn't work is because the current isn't flowing the same direction as that indicated by the voltage polarities. Remember that current can be negative (in the other direction), and you writing +- for the 10 and 100ohms branch whereas the top resistor has -+. Note that the node voltages for the right-side of the circuit are the same, as can be said for the left side. So, by writing -+ on top, and -+ below, you are in effect saying the voltage drop or (increase) are different between the right and left sides depending on which "level" of the circuit, which isn't the case.

One way to solve it is to combine all the parallel resistors into an equivalent resistance, noting that the potential across it is still -+. Then add up the two current sources (they are flowing between the same nodes so it's possible) to get an equivalent current source to get a simplified circuit with only one loop. You would then be able to find V.

 

[Iyafrady]

Is it wrong to think that since the given polarity of the 25ohm resistor is already defined, i should follow the same convention on all the other resistors in which polarity is not defined?..And of course have the current entering the same "terminal" of the resistor?

 

[Defennder]

If the polarity of the resistor is already defined, and if all the elements are in parallel, then you should duplicate the polarity on all the parallel branches.

What I'll do if I were you is to forget all those stuff about assigning voltage polarities and either apply nodal analysis or mesh analysis, or as I suggested earlier combining equivalent resistance. The problem with assigning voltage polarities is that it cannot be done so arbitrarily. Imagine if you have two resistors in series and you arbitrarily decide to assign +- on one and -+ on the other. What does that say about the current flow?

 

[Iyafrady]

uhmm, what does that say about current flow??...i don't know.

 

[Defennder]

Well according to the rule where potential drop is considered positive if current is entering +ve node and negative otherwise, we have the potential drop across both resistors (assume they have same R for simplicity) IR - IR = 0 which of course is nonsensical since the voltage drop across resistors in series adds up, not cancel out each other. You have to be sure that the current is indeed flowing in that direction before you know whether you should add or substract potential drops. Which is why I don't bother with this arbitrary V polarity assignments and instead make use of the nodal/mesh analysis techniques directly.