# 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.

#### Attachments

• Screen shot 2010-02-28 at 9.37.33 PM.png
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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.