How Do You Solve Basic Electric Circuit Analysis Problems with KCL and KVL?

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Discussion Overview

The discussion revolves around solving a basic electric circuit analysis problem using Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL). Participants explore the number of unknown currents, independent KCL equations, and KVL equations that can be derived from a given circuit diagram, while addressing the implications of a wire with no resistance.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant identifies three unknown currents, one KCL equation, and two KVL equations based on their analysis of the circuit diagram.
  • Another participant questions the assumption that currents through resistors R2 and R3 are equal, prompting further exploration of the circuit's configuration.
  • Several participants suggest that the wire with no resistance can be ignored for analysis, proposing to simplify the circuit by connecting the ends of resistors R2, R3, R6, and R7 directly.
  • There is a suggestion that if the wire represents a physical component, it could be treated as a resistor with a very low resistance value for analysis purposes.
  • One participant expresses confidence in solving the problem after considering the previous suggestions.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the treatment of the wire with no resistance, with some proposing it can be ignored while others suggest it may need to be considered as a physical component. The discussion remains unresolved regarding the implications of this wire on the circuit analysis.

Contextual Notes

Participants rely on specific definitions and assumptions about the circuit configuration, including the treatment of the wire with no resistance. The discussion does not resolve how these assumptions affect the overall analysis.

Who May Find This Useful

Students and individuals interested in electric circuit analysis, particularly those learning about KCL and KVL in the context of homework problems.

wompkins
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Homework Statement


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From this circuit diagram assume Vs and R1 through R2 are known.
Find the following:
a) How many unknown currents are there?
b) How many independent equations can be written using KCL?
c) How many independent equations can be derived from KVL equations?


Homework Equations


KCL: Current in - Current out = 0
KVL: Voltage drop around loop should be zero
Ohm's Law: V = iR

The Attempt at a Solution



This problem should not be that difficult but the part that is tripping me up is the middle wire with no resistance in it. Am I correct in assuming that no current will be flowing through it? If so these are the answers I got.

a) 3 unknown currents
b) 1 KCL equation
c) 2 KVL equation

I got (a) from just drawing currents on diagram.

I got (b) from node-voltage which says:
# of KCL eqns = (essential nodes - 1)

Lastly, (c) from mesh-current which says:
# of KVL eqns = branches - (nodes - 1)
 
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Why do you think the currents through R2 and R3 are equal?
 
wompkins said:
Am I correct in assuming that no current will be flowing through it?
You can draw the circuit diagram without that piece of wire. Just join the ends of R2 R3 R6 and R7 together.

If you solve that circuit to find the currents in those four resistors, count the number of essential nodes, etc, you can answer your own question.
 
AlephZero said:
You can draw the circuit diagram without that piece of wire. Just join the ends of R2 R3 R6 and R7 together.
Unless, of course, that wire happens to represent an actual wire in a physical actualization of the circuit. In which case you could think of it as a resistor with value ~0 Ohms for purposes of analyzing the circuit.
 
AlephZero said:
You can draw the circuit diagram without that piece of wire. Just join the ends of R2 R3 R6 and R7 together.

If you solve that circuit to find the currents in those four resistors, count the number of essential nodes, etc, you can answer your own question.

Thank you! I can solve it from there
 

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