What is the relationship between resistors in a circuit?

In summary, the conversation discusses the process of finding equivalent resistance in circuits by simplifying and redrawing the circuit after every step. The markers A and B do not affect the resistance between 42 and 21. The circuit is simplified by combining resistors in series or parallel, and eventually reaching a single resistor. The last circuit requires a conversion from delta to star to solve.
  • #1
Matt O
12
0

Homework Statement


I'm having trouble trying to find equivalent resistance. Here's a picture of some circuits I am trying to simplify (http://puu.sh/ngjMC/38160c3464.png)

38160c3464.png


For example, in circuit a, I can see that the 84 ohm and 105 ohm resistor are in series, and that can be simplified, but what do the markers A and B do to the circuit? Is the result of combining the 84 and 105 in parallel with the 63? And then what is the relationship of the 42 and the 21? Any tips on how to approach these problems are appreciated, thanks.
 
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  • #2
A and B are the points between which the equivalent resistance is asked. For a, I believe your approach is right. Go on combining two resistors at a time(either in series or parallel, whatever is correct).
 
  • #3
cnh1995 said:
A and B are the points between which the equivalent resistance is asked. For a, I believe your approach is right. Go on combining two resistors at a time(either in series or parallel, whatever is correct).
But does it affect the resistance between 42 and 21? Are those in series still?
 
  • #4
The best way to find total resistance in circuits like these is to take it a step at a time and redraw after every step. you have combined the 84 and 105 and noticed that the result is in parallel with the 63. Find your equivalent resistance for those three then redraw. What further simplifications can you make? Eventually you will get to a single resistor.
 
  • #5
Jake 7174 said:
The best way to find total resistance in circuits like these is to take it a step at a time and redraw after every step. you have combined the 84 and 105 and noticed that the result is in parallel with the 63. Find your equivalent resistance for those three then redraw. What further simplifications can you make? Eventually you will get to a single resistor.

Okay, but do the marker points change anything? Is 42 and 21 in series or parallel in diagram a?
 
  • #6
Matt O said:
But does it affect the resistance between 42 and 21? Are those in series still?
They are not in series. Series equivalent of 84 and 105 is in parallel with 63. Their parallel equivalent is?? Can you further simplify?
 
  • #7
cnh1995 said:
They are not in series. Series equivalent of 84 and 105 is in parallel with 63. Their parallel equivalent is?? Can you further simplify?

Ah okay I think Isee, so after that it is in series with the 42 and that combination is in parallel with the 21?
 
  • #8
Matt O said:
Okay, but do the marker points change anything? Is 42 and 21 in series or parallel in diagram a?
The marker points do not change and do not worry about 42 and 21 just yet. Combine the 3 resistors and redraw the circuit. What else can you simplify?
 
  • #9
Matt O said:
Is 42 and 21 in series or parallel in diagram a?
They are neither in series nor in parallel directly. You need to simplify the circuit step by step and find out.
 
  • #10
Matt O said:
Ah okay I think Isee, so after that it is in series with the 42 and that combination is in parallel with the 21?
Right.
 
  • #11
cnh1995 said:
Right.

Okay, makes sense. Thanks a lot for your help
 
  • #12
Matt O said:
Okay, makes sense. Thanks a lot for your help
You can solve all of the circuits above by simplification alone except for the last one which is why it is a bonus. You will need to do a conversion first to solve that.
 
  • #13
Jake 7174 said:
You can solve all of the circuits above by simplification alone except for the last one which is why it is a bonus. You will need to do a conversion first to solve that.

Great, I've been working through them. What type of conversion are you talking about? I can tell it's not the same as the others
 
  • #14
Matt O said:
Great, I've been working through them. What type of conversion are you talking about? I can tell it's not the same as the others
Delta to star..
 
  • #15
cnh1995 said:
Delta to star..

Hmm okay, I'll definitely look into that. Thanks everyone for the help
 
  • #16
Matt O said:
Great, I've been working through them. What type of conversion are you talking about? I can tell it's not the same as the others
It is not the same in that you have resistors that are neither in series or parrallel
Matt O said:
Hmm okay, I'll definitely look into that. Thanks everyone for the help
Star is also referred to as wye
One person may say half a dozen another may say six. They are the same thing.
 

1. What is equivalent resistance?

Equivalent resistance is the total resistance of a circuit that can replace multiple resistors or components in a circuit and produce the same effect. It is a single resistance value that represents the combined effect of all the resistors in a circuit.

2. How do you calculate equivalent resistance?

Equivalent resistance can be calculated using the formula Req = R1 + R2 + ... + Rn, where R1, R2, ..., Rn are the individual resistances in the circuit. This formula applies for resistors in series. For resistors in parallel, the formula is 1/Req = 1/R1 + 1/R2 + ... + 1/Rn.

3. Why is equivalent resistance important?

Equivalent resistance is important because it simplifies the analysis and calculation of complex circuits. It allows us to replace multiple resistors with a single equivalent resistor, making circuit analysis more efficient and practical.

4. How does equivalent resistance affect current and voltage?

Equivalent resistance affects current and voltage in a circuit by determining the flow of electrons and the potential difference across the circuit. A higher equivalent resistance means lower current flow and lower potential difference, while a lower equivalent resistance leads to higher current flow and higher potential difference.

5. What is the difference between series and parallel equivalent resistance?

In series circuits, the equivalent resistance is the sum of all the individual resistances, while in parallel circuits, the equivalent resistance is the reciprocal of the sum of the reciprocals of all the individual resistances. In series circuits, the equivalent resistance is always greater than any individual resistance, while in parallel circuits, the equivalent resistance is always less than any individual resistance.

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