Question

Calculate the current through the individual resistors in the following circuit diagram. Please show ALL work.

50 Ω 20 Ω 30 Ω + 12V 12 13 15 Ω 20 Ω 30 V (14) i4 15 - 80 Ω 20 V 60 Ω

Answer 1

From the given diagram
using kirchoff's law
for i1, 30 = 50i1 + 20i1 - 20i2 + 80i1 - 80i4
for i2, 20i2 - 20i1 + 30i2 - 30i3 + 15i2 - 15i4
for i3, 12 = 30i2 - 30i3 + 20i5 - 20i3
for i4, 20 = 80i4 -80i1 + 15i4 - 15i2
for i5, 20 = -60*i5 + 20*i3 - 20*i5

Solving these equations simultaneously we get
so we convert the equations in to matrix form
Ai = B
i = [A]inv * B
where [A]inv is inverse of [A]
from the equations
[150 -20 0 -80 0]
[-20 65 -30 -15 0]
[A] = [0 30 -50 0 20]
[-80 -15 0 95 0 ]
[0 0 20 0 -80]
  
and [i] = [i1]
[i2]
[i3]
[i4]
[i5]
  
so form matrix method
  
i1 = 0.7039257 A
i2 = 0.3470378 A
i3 = -0.14641922 A
i4 = 0.858101356 A
i5 = -0.2866048 A