Solve KCL/MESH Problem: E=15V, R1=20k, R2=4.7k, R3=10k

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Discussion Overview

The discussion revolves around solving a circuit problem using Kirchhoff's Current Law (KCL) and Mesh Analysis. Participants are tasked with determining the currents I_1, I_2, and I_3 in a circuit with given voltage and resistance values. The focus includes the application of KCL and KVL equations, as well as the potential use of Norton equivalent circuits.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • The original poster attempts to apply KCL and proposes loop equations but questions their correctness.
  • One participant points out an error in the original equations, stating that the voltage across R1 should be R1*I1, not R1(I1 + I3), and clarifies that KCL applies to currents, not voltages.
  • Another participant agrees with the previous correction and suggests combining resistors to find the current from the supply, mentioning that Norton equivalent circuits may simplify the analysis.
  • A later reply suggests applying KVL at two meshes to derive two equations with two variables, indicating a potential method to solve the problem.

Areas of Agreement / Disagreement

Participants generally agree that there are errors in the original equations and that KCL is applicable. However, there is no consensus on the best approach to solve the problem, with multiple methods proposed, including KCL, KVL, and Norton equivalents.

Contextual Notes

The discussion highlights potential confusion between KCL and KVL, and the limitations of the original equations presented. The number of unknowns versus equations is also noted as a concern.

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Homework Statement



circuit-1.jpg


Determine I_1 I_2 I_3
When
E = 15V
R1 = 20k ohms
R2 = 4.7k ohms
R3 = 10k ohms

Homework Equations



KCL equation

The Attempt at a Solution



i tried to find using KCL.. is my equation right?
Loop equation 1:
EB + I3R3 + R1(I3 + I1) = 0

Loop equation 2:
R1(I1 + I3) + R2(I1 – I2) = 0

Loop equation 3:
EB + I3R3 + I2R2 = 0

can i use MESH analysis... but there are three unknowns and if i use mesh, i can only have 2 equations with 3 unknowns
 
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Welcome to PF.

There is a problem with your equations.

The voltage across R1 is is simply R1*I1, not R1(I1 + I3), because the current flowing through R1 is simply I1.

Likewise, the voltage across R2 is R2*I2.

Also, these are KVL equations for voltage, not KCL which would apply to currents. KCL says that the sum of all currents entering a node is zero, and will be useful here.

Note, another way to solve this would be to use the rules for combining resistors in parallel and series.
 
I agree with Redbelly98, I think you're confusing KVL for KCL. See if you can combine the resistors to find the current coming out of the supply. From there, I think it's easier if you find the http://en.wikipedia.org/wiki/Norton_equivalent" equations. See link for quick wikipedia articles on them. Mesh analysis will work just fine here as well, but I think it's more obvious using Norton equivalent.
 
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u can apply kvl at the 2mishes and get 2equa., in 2variables .then solve them
 

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