For the resistor network in the picture, use loop currents to find the current through the 4Ω resistor and the change in voltage E across the current source.
Circuit Attached Below .
- Kirchoffs Laws
- Loop Current Method
The Attempt at a Solution
Firstly I divided the circuit into 3 loops with 3 currents.
- Top left Loop, Current A
- Top right Loop, Current B
- Bottom Loop, Current C
- Voltage Change,E, across the current source
- Current A
- Current B
- Current C
Now I apply Kirchoffs laws for every loop. I go around in a counter clockwise manner and get the total drop in voltage for each.
- Loop A: -E+A+2(A-C)=0
- Loop B: E+(B-C)+2(B)=0
- Loop C: 12+(C-B)+2(C-A)+4C=0
Now i have 3 equations, but 4 unknowns,
So i need another equation coming from the current provided from the current source to get a system of equations and solve it.
But i know that the current source provides a current of 1amp for the loop, however this is where I am not sure how to proceed,
does it mean that both A and B = 1 or A=1 only? How do i know which current the source affects?
I proceeded with the assumption that both A and B both equal one, but got an overdetermined system with no solution.
On second though maybe, both currents are related by let's say, the source gives out current = 1amp, so loop 1 and 2 share this current so, currents A+B=1 sort of thing? Proceed by substituting A=1-B into the system of equations and get 3 unknowns 3 equations?
Just need some checking on this fact and the rest of the problem is pretty straight forward.
Thanks in Advance.