Combined resistance in this circuit

[Eitan Levy]

Homework Statement

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.

 

[phinds]

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

 

[Eitan Levy]

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.

 

[phinds]

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.

 

[Eitan Levy]

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.

 

[phinds]

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?

 

[gneill]

...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?

 

[Eitan Levy]

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.

 

[Eitan Levy]

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.

 

[phinds]

I didn't think I should do this.

I did combine the resistors ...

So you don't think you should combine the resistors but you did combine the resistors?

 

[phinds]

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]

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.

 

[Eitan Levy]

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.

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!