Applying Kirchoff's law to circuit which only has cells

[mahela007]

Homework Statement

Find the Voltage across A B in the following circuit. Each cells has negligible internal resistance and an EMF of E volts.
(First diagram in the attached picture)

Homework Equations

I'm trying to use Kirchoff's second law.

The Attempt at a Solution

Now, if I traverse the RSTU loop in the clockwise direction, I find that V_AB = 2E.
Similarly, if I traverse the loop RQPU, I also get V_AB = 2E.
In this case, traversing either loop gives the same answer for V_AB

But what if the polarity of cell TS (the top most cell) was reversed as in the second diagram?
In this case, applying Kirchoff's law to loops RSTU and RQPU yields different results for V_AB.. so in such a case, what is the actual value of V_AB

 

[Quinzio]

The second case has no solution. It would imply an infinite current flowing in the circuit.
It is impossible to determine Vab.

 

[tiny-tim]

hi mahela007!

sorry, but that makes no sense

Kirchhoff's rules require current, and you haven't included any

(and there's no such thing as circuits or cells without resistance, you have to include a resistance somewhere on each loop)

 

[mahela007]

Do we need to consider the current? Don't the cells maintain a potential difference equal to their EMF because they don't have internal resistance?

 

[tiny-tim]

all cells have internal resistance!

(even you said "negligible" … that's not zero!)

 

[mahela007]

lol... ok then.
Let's say for theoretical purposes that a cell had 0 resistance.
Kirchoff's second law says that the algebraic sum of potential differences around a closed loop is 0. The (imaginary) batteries maintain a constant voltage across their terminals. So shouldn't we be able to apply K's law? (regardless of the current that is flowing in this case)

EDIT:
WHOOPS.
I was wondering about this for all of about 5 mins.. then it dawned on me that this model is a violoation of the principle of the conservation of energy. If charge is flowing from one terminal to the other, then some energy must be liberated because of the potential difference. If there is no resistance, no energy can be liberated..

Thanks for all your help.

 

[Quinzio]

lol... ok then.
Let's say for theoretical purposes that a cell had 0 resistance.
Kirchoff's second law says that the algebraic sum of potential differences around a closed loop is 0.

Ok, so try to apply it to the outer loop. You have that Va+Vb=0
Let's say Va=Vb=5V, so we have 10=0 ?