I have the following circuit and i want to look for the current and voltage across R(adsbygoogle = window.adsbygoogle || []).push({}); _{1}:

Let's ignore the numeric value for v_{1}, v_{2}and R_{1}and generalize them.

If i apply Mesh Analysis i get the following formulas:

[tex]v_1 = (i_1 + i_2) R_1[/tex]

[tex]v_2 = (i_1 + i_2) R_1[/tex]

And if i apply Crammer's rule i get:

[tex]\Delta = R_1^2 - R_1^2 = 0[/tex]

[tex]\Delta_1 = v_1 R_1 - v_2 R_1[/tex]

[tex]\Delta_2 = v_1 R_1 - v_2 R_1[/tex]

So, if i want to get i_{1}, i_{2}:

[tex]i_1 = \frac{\Delta_1}{\Delta} = \frac{v_1 R_1 - v_2 R}{0}[/tex]

[tex]i_2 = \frac{\Delta_2}{\Delta} = \frac{v_2 R_1 - v_1 R_1}{0}[/tex]

And if v_{1}, v_{2}are equal it comes even worse!:

[tex]i_1 = i_2 = \frac{(0)(0) - (0)(0)}{0}[/tex]

As for the voltage across R_{1}:

[tex]v_R1 = (i_1 + i_2) R_1 = (\frac{v_1 R_1 - v_2 R}{0} + \frac{v_2 R_1 - v_1 R_1}{0}) R_1 = \frac{0}{0} R_1[/tex]

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# How do i solve the following circuit?

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