Application of Circuit laws (KCL and KVL)

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Homework Help Overview

The discussion revolves around calculating the resistance of a combination of resistors using Kirchhoff's circuit laws (KCL and KVL). Participants are exploring the relationships between currents and voltages in the circuit.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to apply KVL to relate the currents and voltages in the circuit. There are discussions about expressing total current in terms of individual currents and substituting these into the resistance formula.

Discussion Status

The conversation is ongoing, with some participants providing guidance on how to manipulate equations to express current in terms of other variables. There is recognition of a potential oversight in the original poster's approach, but no consensus has been reached on a complete solution.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. There is an emphasis on deriving relationships rather than providing direct answers.

hms.tech
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Homework Statement


Calculate the resistance of this combination of resistors

Homework Equations



V=IR

The Attempt at a Solution



By using KVL :

V= 3[itex]I_{5}[/itex] = [itex]I_{2}[/itex] = 2[itex]I_{4}[/itex]
I = [itex]I_{1}[/itex] + [itex]I_{2}[/itex]
[itex]I_{3}[/itex] = [itex]I_{2}[/itex] + [itex]I_{4}[/itex]
[itex]I_{1}[/itex] = [itex]I_{5}[/itex] + [itex]I_{4}[/itex]
I = [itex]I_{3}[/itex] + [itex]I_{5}[/itex]Now the final result could be obtained by the simple equation : R =V/I (this is where my progress stagnates)
 

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Your first equation relates currents I2, I4, and I5 to the potential across the circuit. Now, if you take your last equation and make substitutions so that you express I in terms of those same currents in the first expression, I think you'll get somewhere.
 
You mean like this :

I = [itex]I_{5}[/itex] + [itex]I_{2}[/itex] + [itex]I_{4}[/itex]

Thus R = V/I

that does not solve the problem ...
 
hms.tech said:
You mean like this :

I = [itex]I_{5}[/itex] + [itex]I_{2}[/itex] + [itex]I_{4}[/itex]

Thus R = V/I

that does not solve the problem ...

But you can substitute your expressions for those currents from your first equation...
 
Oh yes, I overlooked this .
Thanks you
 

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