Combined resistance in this circuit

In summary, this person is trying to find the combined resistance of two switches when they are closed. They found that the answer is 4Ω.
  • #1
Eitan Levy
259
11

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.
 

Attachments

  • upload_2017-12-31_21-5-20.png
    upload_2017-12-31_21-5-20.png
    2.9 KB · Views: 734
Physics news on Phys.org
  • #2
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
 
  • #3
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.
 
  • #4
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.
 
  • #5
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.
 
  • #6
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?
 
  • #7
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?
 
  • #8
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.
 
  • #9
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!
 

1. What is combined resistance in a circuit?

Combined resistance in a circuit refers to the total resistance encountered by the flow of current through the circuit. It is calculated by adding all the individual resistances in a series circuit or by using the reciprocal method in a parallel circuit.

2. How is combined resistance calculated in a series circuit?

In a series circuit, combined resistance is calculated by simply adding all the individual resistances together. This is because the current has to pass through each component in succession, resulting in an additive effect on the total resistance.

3. How is combined resistance calculated in a parallel circuit?

In a parallel circuit, combined resistance is calculated using the reciprocal method. This involves finding the reciprocal of each individual resistance, adding them together, and then taking the reciprocal of the sum. This method takes into account the fact that the current is divided among the different paths in a parallel circuit.

4. What happens to combined resistance when resistors are added in series?

When resistors are added in series, the combined resistance increases. This is because the current has to pass through each resistor in succession, resulting in an increase in the overall resistance encountered by the current.

5. What happens to combined resistance when resistors are added in parallel?

When resistors are added in parallel, the combined resistance decreases. This is because the current is divided among the different paths, resulting in a decrease in the overall resistance encountered by the current.

Similar threads

  • Introductory Physics Homework Help
Replies
9
Views
1K
  • Introductory Physics Homework Help
2
Replies
42
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
818
  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
24
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
2K
  • Introductory Physics Homework Help
Replies
10
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
256
  • Introductory Physics Homework Help
Replies
7
Views
910
  • Introductory Physics Homework Help
Replies
13
Views
1K
Back
Top