How Do You Solve a Parallel Circuit Problem with Unequal Currents?

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Discussion Overview

The discussion revolves around solving a problem related to a parallel circuit with three resistors (R1, R2, R3) that have unequal currents (I1, I2, I3). Participants are attempting to calculate the values of the resistors given their equivalent resistance and the relationships between the currents.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant presents the problem and attempts to use the parallel circuit equation to find R1, R2, and R3, but expresses uncertainty about their solution.
  • Another participant requests a schematic or diagram to better understand the problem context.
  • There is a discussion about the relationship between current and resistance, with some participants stating that higher current corresponds to lower resistance.
  • Participants note that the equivalent resistance of the parallel combination is less than the smallest individual resistor and that the voltage across all resistors is the same in a parallel circuit.
  • One participant questions how to apply Ohm's Law without knowing the voltage, while others suggest using the relationships among the currents to find the resistances.

Areas of Agreement / Disagreement

Participants generally agree on the principles of parallel circuits and the relationships between current and resistance, but there is uncertainty regarding the application of these principles to the specific problem presented. The discussion remains unresolved as participants explore different approaches without reaching a consensus.

Contextual Notes

There are limitations in the problem statement, such as the lack of a voltage value and a schematic, which may affect the ability to apply Ohm's Law directly. The relationships among the currents are established, but the exact values of the resistors remain undetermined.

Peter Ke
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Homework Statement


Resistor R1, R2, R3 are connected in parallel, have an equivalent resistance of 720(ohms). The currents are labeled I1, I2,and I3. I2 is 3x the value of I1, and I3 is 6x the value of I1. Calculate R1, R2, R3.

Homework Equations


I used the parallel circuit equation. 1/RT=1/R1+1/R2...

The Attempt at a Solution


[/B]
I tried to solve it like this...

1/720= 1/R1+1/(1/3R1)+1/(1/6R1)---> 720=R1+3R1)+6R1-----> 720= 10R1-----> R1=72 ohms.
I know I made a mistake or I have been following the wrong path. Please help I really don't understand this question. Thank You!
 
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Peter Ke said:

Homework Statement


Resistor R1, R2, R3 are connected in parallel, have an equivalent resistance of 720(ohms). The currents are labeled I1, I2,and I3. I2 is 3x the value of I1, and I3 is 6x the value of I1. Calculate R1, R2, R3.

Homework Equations


I used the parallel circuit equation. 1/RT=1/R1+1/R2...

The Attempt at a Solution


[/B]
I tried to solve it like this...

1/720= 1/R1+1/(1/3R1)+1/(1/6R1)---> 720=R1+3R1)+6R1-----> 720= 10R1-----> R1=72 ohms.
I know I made a mistake or I have been following the wrong path. Please help I really don't understand this question. Thank You!
Can you upload a copy of the problem/schematic? :smile:
 
berkeman said:
Can you upload a copy of the problem/schematic? :smile:

I'm so sorry, this was a word problem that came from a classwork that the teacher gave me. There was no diagram that came with it.
I have seen one person who tried to solve it in this website ---> https://answers.yahoo.com/question/index?qid=20140911191648AArMp36
but he didn't explain it, he just showed his equation so I still didn't understand how he arrived on his answers.

If you could help, then thank you!
 
Peter Ke said:
1/720= 1/R1+1/(1/3R1)+1/(1/6R1)
With the same voltage across the resistors (parallel circuit), when the current is higher, is the resistance higher or lower?
Then look at the equation you generated. Does it indicate higher or lower resistances for the associated currents?
 
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When the current is higher the resistance is lower because current and resistance are inversely proportional.
Based on what you said, my equation indicates that it has higher resistance when I simplify it.
 
Peter Ke said:
When the current is higher the resistance is lower because current and resistance are inversely proportional.
Based on what you said, my equation indicates that it has higher resistance when I simplify it.
Equivalent resistance of the parallel combination is less than the least of R1, R2 and R3.
Voltage across all the resistors is same since they are in parallel. Use Ohm's law to find the resistances.
 
Yea but the amount of voltage is not given so how do I even use Ohm's Law?
 
Peter Ke said:
Yea but the amount of voltage is not given so how do I even use Ohm's Law?
V=IR..
So, I1R1=I2R2=I3R3..
You know the relation amongst I1, I2 and I3.
 
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cnh1995 said:
V=IR..
So, I1R1=I2R2=I3R3..
You know the relation amongst I1, I2 and I3.
Thank you so much! I got it!
 

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