The
set of equations from the assigned problem will vary, here is one possible
set.
V1−R1I1−R3I3=0(13)
−R2I2−V2+R3I3=0(14)
V2−V3−R6I6+R5I5=0(15)
R4I4−R5I5=0(16)
−V4−R4I4=0(17)
I1−I2−I3=0(18)
This
set of equations can be converted to the following matrix equation:
⎡⎣⎢⎢⎢⎢⎢⎢⎢⎢R1000010−R2000−1R3R3000−1000R4−R4000−R5R50000R6000⎤⎦⎥⎥⎥⎥⎥⎥⎥⎥⎡⎣⎢⎢⎢⎢⎢⎢⎢⎢I1I2I3I4I5I6⎤⎦⎥⎥⎥⎥⎥⎥⎥⎥=⎡⎣⎢⎢⎢⎢⎢⎢⎢⎢V1V2V2−V30V40⎤⎦⎥⎥⎥⎥⎥⎥⎥⎥(19)
The
answers are
I1=−0.091(20)
I2=−0.455(21)
I3=0.364(22)
I4=−1(23)
I5=0.8(24)
I6=0.5(25)
It
should be noted that for the circuit in the second figure, currents I1 through I3 are
the same as for the first figure, and it may be interesting to discuss
with students why that should be the case.