Solving a Simple Circuit involving Current Source by the Loop Current Method

[Lemm]

Homework Statement

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 .

Homework Equations

• Kirchoffs Laws
• Loop Current Method
• V=IR

The Attempt at a Solution

Firstly I divided the circuit into 3 loops with 3 currents.

1. Top left Loop, Current A
2. Top right Loop, Current B
3. Bottom Loop, Current C

Looking For

• 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.

 

[ehild]

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.

There are two Kirchhoff's rules, one for the currents at nodes, the other for voltages in a loop.
You need to know them, and then it is not a possibility but the truth what your "second thought" is.

ehild

 

[simpleton]

In case you want to check your answer, the currents are 6/11 A, 17/11 A and 23/11 A respectively. You have to use both Kirchoff's Loop Rule and Current Rule. At least that's what I did.