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

In summary, the conversation discusses using loop currents to find the current through a resistor and the voltage change across a current source in a resistor network. The circuit is divided into three loops and Kirchoff's laws are applied to each loop. However, an additional equation is needed to solve the system of equations, which can be obtained from the given current provided by the current source. The solution is obtained by substituting one of the currents in terms of the other two and using both Kirchoff's Loop Rule and Current Rule. The final currents are 6/11 A, 17/11 A, and 23/11 A.
  • #1
Lemm
22
0

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.
 

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  • #2
Lemm said:

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
 
  • #3
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.
 

1. What is the Loop Current Method for solving a simple circuit?

The Loop Current Method is a technique used to analyze and solve circuits that contain current sources. It involves assigning a direction to the current flow in each loop of the circuit and then using Kirchhoff's Voltage Law to write equations for the voltage drops around each loop.

2. How do you assign directions to the current flow in a circuit for the Loop Current Method?

To assign directions to the current flow, you can follow these steps:

  • Choose a starting point in the circuit and label it as the reference node.
  • Select a direction for the current flow in each loop, starting from the reference node.
  • Label each loop with the direction of the current flow.
  • Ensure that the current direction in each loop is consistent with the voltage drops in that loop.

3. How do you use Kirchhoff's Voltage Law in the Loop Current Method?

Kirchhoff's Voltage Law states that the algebraic sum of all voltage drops around a closed loop in a circuit is equal to zero. In the Loop Current Method, you will write equations for each loop using this law and then solve for the unknown currents.

4. Can the Loop Current Method be used for circuits with multiple current sources?

Yes, the Loop Current Method can be used for circuits with multiple current sources. In these cases, you will assign a separate loop for each current source and use Kirchhoff's Voltage Law to write equations for each loop. Then, you can solve the resulting system of equations to find the unknown currents.

5. Are there any limitations to using the Loop Current Method to solve circuits?

The Loop Current Method is most effective for simple circuits with a small number of current sources. It may become more complicated and time-consuming for circuits with a large number of current sources or complex configurations. In these cases, other circuit analysis techniques such as nodal analysis may be more suitable.

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