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Homework Statement
In the circuit (see attachment) we have 2 sources. If we decrease the EMF of the first source (ε_{1}) by 1.5V, the current changes in every branch of the circuit. How does the EMF of the source ε_{2} has to be changed, so that the current through the ε_{1} source would be the same as previously?
Homework Equations
Kirchhoff's laws
The Attempt at a Solution
I guess what we need to do here is to find the dependency of ε_{1} on ε_{2}. Is using the Kirchhoff's equations the best way here? I wrote down such eq:
[itex]
I_3R + I_1r_1 + I_5R = \epsilon_1
[/itex]
[itex]
3I_4R + I_6R + I_1r_1 = \epsilon_1
[/itex]
[itex]
I_2r_2 + I_6R  I_5R = \epsilon_2
[/itex]
[itex]
I_3 + I_4 = I_1
[/itex]
[itex]
I_5+I_6 = I_1
[/itex]
[itex]
I_3 = I_5 + I_2
[/itex]
[itex]
I_4 + I_2 = I_6
[/itex]
Here r_{1}, r_{2}  internal resistances of the sources (since there is current flowing through the sources, they must have internal resistances, right?)
I_{3}  top left resistor
I_{5}  down left resistor
I_{4}  top right resistor
I_{6}  down right resistor
I_{1}  ε_{1} current
I_{2}  ε_{2} current
But couldn't solve the system :/
Maybe there is a better way to do this? It seems to me there should be something simpler than system of 8 equations?
Any help appreciated!
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