Calculate the equivalent resistance in the Figure

In summary, the conversation discusses identifying resistors in parallel and simplifying a circuit by combining resistors. The correct answer has 3 resistors in parallel, not just 2. The diagonal wire creates a short circuit for R2, and the equivalent resistance can be found by checking the ends of the resistors. The final combination is R1, R3, and R4 in parallel.
  • #1
Kelsi_Jade
59
0

Homework Statement


upload_2017-3-27_9-10-48.png


Homework Equations

/ 3. The Attempt at a Solution
Here is my attempt from the homework assignment. It doesn't appear that I got any points for this question and was hoping to get a little help in correcting my issues or pointed in the right direction to start over. [/B]
upload_2017-3-27_9-16-8.png
 
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  • #2
Can you spot the resistors in parallel? Parallel resistors will have their ends connected between the same two points.

The red diagram is the correct one. Is that the provided answer?
 
  • #3
I'm not sure what the correct answer is. I'm also confused in my TA's diagram why it has 4 resistors?
There only 2 resistors that are in parallel, right?
 
  • #4
Kelsi_Jade said:
There only 2 resistors that are in parallel, right?
No.
There is one more. Look carefully.
 
  • #5
OK, thinking out loud here:
It looks like he was simplifying the circuit?
I can see that we should be able to combine resistors to make an easier diagram (which is how we go from 5 Resistors to 4 Resistors in the red). I'm a little confused on the orientation and how we have 3 Resis. in parallel.

I doodled it out but I can't see how it is simplified to make 3 resis. in parallel instead of the 2 obvious resistors.
Why isn't R5 in series with the R2 and R3,4 combination now?
upload_2017-3-27_9-54-4.png
 
  • #6
Kelsi_Jade said:
in parallel instead of the 2 obvious resistors.
How is R3 connected to R4? Check their ends.
 
  • #7
They're connected in series, so can't you add them together and make it equivalent to a resistor with a sum of their resistances?
eg. R3,4=R3 + R4
and then this new resistor is in series with R1?
 
  • #8
Kelsi_Jade said:
They're connected in series
No. Check their ends. Aren't they connected between the "same" two points?
 
  • #9
Is it because of the diagonal line, does that indicate that the first end point of R3 is the same end as the first end point of R4?
 
  • #10
Kelsi_Jade said:
Is it because of the diagonal line, does that indicate that the first end point of R3 is the same end as the first end point of R4?
Exactly!
 
  • #11
Sweet!
OK, so now I have the diagram looking like the figure below, but where does the R5 fit in? It's in series with R2, R3, and R4 also, right?
So, is it R1 and R5 that can be combined in series like I said before?
upload_2017-3-27_10-49-48.png
 
  • #12
Kelsi_Jade said:
Sweet!
OK, so now I have the diagram looking like the figure below, but where does the R5 fit in? It's in series with R2, R3, and R4 also, right?
So, is it R1 and R5 that can be combined in series like I said before?
View attachment 115123
R2 is not in parallel with R3 and R4. In fact, you'll see something interesting about R2.

Which three are in parallel?
 
  • #13
R1 is in series with R2 which is in series with R5, right?
 
  • #14
Kelsi_Jade said:
R1 is in series with R2 which is in series with R5, right?
No.

Which three are in parallel?

What does the diagonal wire do to R2?
 
  • #15
The diagonal would cause a short circuit so there would be no resistance through R2
because the current would go through the path of least resistance, the diagonal wire
 
  • #16
Kelsi_Jade said:
The diagonal would cause a short circuit so there would be no resistance through R2
because the current would go through the path of least resistance, the diagonal wire
Right.
Which three are in parallel?

I believe you'll be able to find the equivalent resistance now.
 
  • #17
Oh gosh, Then R1, R3, and R4 are the parallel resistors
Then, 1/Rtot=1/R1 + 1/R3 + 1/R4
 
  • #18
Kelsi_Jade said:
Oh gosh, Then R1, R3, and R4 are the parallel resistors
Then, 1/Rtot=1/R1 + 1/R3 + 1/R4
No.
(And that leaves only one combination:biggrin:.)

Check the ends of the resistors. If they are connected between the same two points, they are in parallel.
 
  • #19
Oooh so would the points work out equivalently like this?
upload_2017-3-27_11-46-45.png
 
  • #20
Kelsi_Jade said:
Oooh so would the points work out equivalently like this?
View attachment 115124
There you go!
 
  • #21
FINALLY! Thanks for all of your help (and patience).
 
  • #22
Kelsi_Jade said:
FINALLY! Thanks for all of your help (and patience).
You're welcome!
 

Related to Calculate the equivalent resistance in the Figure

What is the purpose of calculating the equivalent resistance in this figure?

The purpose of calculating the equivalent resistance in this figure is to determine the total resistance of a circuit, which is necessary for understanding and analyzing its behavior.

How do you calculate the equivalent resistance in a circuit?

To calculate the equivalent resistance, you need to identify all the resistors in the circuit and determine if they are connected in series or parallel. For resistors in series, simply add their individual resistances. For resistors in parallel, use the formula 1/Req = 1/R1 + 1/R2 + ... + 1/Rn, where Req is the equivalent resistance and R1, R2, etc. are the individual resistances. Once you have all the resistances added, take the reciprocal to find the equivalent resistance.

What is the difference between series and parallel connections?

Series connections involve connecting components one after the other in a single loop, while parallel connections involve connecting components side by side so that they share the same two points. In series connections, the current remains the same throughout the circuit, while in parallel connections, the voltage remains the same.

Why is it important to know the equivalent resistance in a circuit?

Knowing the equivalent resistance in a circuit is important because it allows us to calculate the total current and voltage in the circuit. It is also useful for determining the power dissipated by the resistors and for troubleshooting any issues in the circuit.

Can the equivalent resistance ever be greater than the individual resistances in a circuit?

No, the equivalent resistance can never be greater than the individual resistances in a circuit. This is because adding more resistors in series will always increase the total resistance, while adding more resistors in parallel will always decrease the total resistance. The equivalent resistance is always equal to or less than the individual resistances in a circuit.

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