- #1
cshum00
- 215
- 0
I have the following circuit and i want to look for the current and voltage across R1:
Let's ignore the numeric value for v1, v2 and R1 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 i1, i2:
[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 v1, v2 are equal it comes even worse!:
[tex]i_1 = i_2 = \frac{(0)(0) - (0)(0)}{0}[/tex]
As for the voltage across R1:
[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]
Let's ignore the numeric value for v1, v2 and R1 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 i1, i2:
[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 v1, v2 are equal it comes even worse!:
[tex]i_1 = i_2 = \frac{(0)(0) - (0)(0)}{0}[/tex]
As for the voltage across R1:
[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]