Combined resistance in this circuit

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Homework Help Overview

The discussion revolves around calculating the combined resistance in a circuit when a switch is closed. Participants are examining the relationship between current and resistance using Ohm's law, and there is a focus on the implications of combining resistors in different configurations.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the calculation of combined resistance using current values derived from the circuit. There are questions about the validity of using total current to find resistance and the necessity of combining resistors correctly. Some express confusion about the application of methods when the switch is closed versus open.

Discussion Status

The discussion is ongoing, with participants providing insights and questioning each other's reasoning. There is no clear consensus on the correct approach to calculating the combined resistance, and multiple interpretations of the problem are being explored.

Contextual Notes

Some participants mention the need for clarity on how to combine resistors in the circuit configuration presented, and there are references to potential discrepancies in the provided answer of 4Ω compared to calculated values.

Eitan Levy
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Homework Statement


upload_2017-12-31_21-5-20.png

What is the combined resistance when the switch is closed?

Homework Equations


IR=V

The Attempt at a Solution


I found that I1=5.2A and that I2=9.1A. The answers follow suit.
Now I thought that calculating the combined resistance with 60/(I1+I2) would be correct, however the answer is 4Ω.
Can anybody help me out in this? Thanks.
 

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Eitan Levy said:

Homework Statement


View attachment 217674
What is the combined resistance when the switch is closed?

Homework Equations


IR=V

The Attempt at a Solution


I found that I1=5.2A and that I2=9.1A. The answers follow suit.
Now I thought that calculating the combined resistance with 60/(I1+I2) would be correct, however the answer is 4Ω.
Can anybody help me out in this? Thanks.
Show your work. Show how you combine various resistors to get the total resistance
 
phinds said:
Show your work. Show how you combine various resistors to get the total resistance
I didn't think I should do this. Why is it wrong to just divide the voltage by the total current? This gives 4.2 instead of 4. We didn't study how to really combine the resistors when they are connected like this.
 
Eitan Levy said:
I didn't think I should do this. Why is it wrong to just divide the voltage by the total current? This gives 4.2 instead of 4. We didn't study how to really combine the resistors when they are connected like this.
You have computed something with the switch open and you are applying it when the switch is closed. That just flat does not work. You HAVE to figure out the combined resistance with the switch closed.
 
phinds said:
You have computed something with the switch open and you are applying it when the switch is closed. That just flat does not work. You HAVE to figure out the combined resistance with the switch closed.
What do you mean? These currents are for when the switch is CLOSED, not open.
 
Eitan Levy said:
What do you mean? These currents are for when the switch is CLOSED, not open.
They how could you possibly have gotten it without combining the resistors?
 
Eitan Levy said:
...however the answer is 4Ω.
How do you know that the answer is 4Ω ? Was this a multiple choice question? Or perhaps they want the result rounded to an appropriate number of significant digits?
 
phinds said:
They how could you possibly have gotten it without combining the resistors?
I thought it doesn't matter how I reached those currents. I did combine the resistors in order to reach those current, and they are correct.
 
gneill said:
How do you know that the answer is 4Ω ? Was this a multiple choice question? Or perhaps they want the result rounded to an appropriate number of significant digits?
Maybe they did but it would be very unusual. This is the answer written in the answers as correct.
 
  • #10
Eitan Levy said:
I didn't think I should do this.

Eitan Levy said:
I did combine the resistors ...
So you don't think you should combine the resistors but you did combine the resistors?
 
  • #11
Using a delta-wye transform I get an equivalent resistance that is compatible with the sum of the currents you stated, and of course, it's not 4 ohms. Since you combined the resistances, you MUST have gotten the same thing I did, else you could not have gotten the right total current.
 
  • #12
Eitan Levy said:
I found that I1=5.2A and that I2=9.1A. The answers follow suit.
Now I thought that calculating the combined resistance with 60/(I1+I2) would be correct, however the answer is 4Ω.
This method is correct provided that your current values are correct. If, for correct current values, your result doesn't match the supplied answer for the total resistance with the appropriate number of significant figures for the given data, then that supplied "correct" value is not accurate.
 
  • #13
phinds said:
Using a delta-wye transform I get an equivalent resistance that is compatible with the sum of the currents you stated, and of course, it's not 4 ohms. Since you combined the resistances, you MUST have gotten the same thing I did, else you could not have gotten the right total current.
gneill said:
This method is correct provided that your current values are correct. If, for correct current values, your result doesn't match the supplied answer for the total resistance with the appropriate number of significant figures for the given data, then that supplied "correct" value is not accurate.
Alright, thanks for the help!
 

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