Equivalent Resistance Homework: Help Needed!

  • Thread starter yecko
  • Start date
  • Tags
    Resistance
In summary: So their combined voltage is twice that of the 9kΩ resistors, or 18kΩ.In summary,The student is having difficulty understanding the homework statement and is requesting help. They are not able to identify the circuit to be parallel or series in order to get the equivalent resistance, and are asking for an alternative method. They are also unfamiliar with the Δ-Y transformations and are looking for a picture of the circuit.
  • #1
yecko
Gold Member
279
15

Homework Statement


螢幕快照 2017-12-13 上午11.32.52.png


Homework Equations


parallel(two shared nodes in two sides), series resistor(one shared node between 2 resistors)

The Attempt at a Solution


2017-12-13-PHOTO-00000175.jpg

I can't identify the circuit to be parallel or series in order to get the equivalent resistance.
how should I finish the question?

( correction: answer=6kΩ)
as i will have exam few hours later... please help! thanks!
 

Attachments

  • 螢幕快照 2017-12-13 上午11.32.52.png
    螢幕快照 2017-12-13 上午11.32.52.png
    17.1 KB · Views: 981
  • 2017-12-13-PHOTO-00000175.jpg
    2017-12-13-PHOTO-00000175.jpg
    32.1 KB · Views: 924
Physics news on Phys.org
  • #2
It's against my religion to offer full solution but I can give you a hint:
If you look how the 12 ##k\Omega## is connected, you notice that there is no voltage across it, so, no current. Just remove it from the circuit and continue.
 
  • #3
Henryk said:
If you look how the 12 kΩkΩk\Omega is connected, you notice that there is no voltage across it,
you should be right, when I shorted the 12 kΩ, i can get the correct answer of 6kΩ
but why no voltage across it?
 
  • #4
螢幕快照 2017-12-13 下午12.39.19.png

what if this kind of asymmetric circuit?
 

Attachments

  • 螢幕快照 2017-12-13 下午12.39.19.png
    螢幕快照 2017-12-13 下午12.39.19.png
    6.8 KB · Views: 514
  • #5
Convert the upper triangle from delta to star.
 
  • #6
jaus tail said:
Convert the upper triangle from delta to star.
what do you mean by "delta" and "star"?
(i have never learned wheatstone bridge...)
 
  • #7
Have you been taught star-delta resistance transformation?
Or only Rseries and Rparallel?
 
  • #8
Only R series and parallel...
 
  • #9
yecko said:
Only R series and parallel...
If you are unfamiliar with the Δ-Y transformations (It would be worth your while to look it up!), then an alternative is to apply a voltage source across AB and solve the circuit for the current that the source produces. Ohm's law will then tell you the effective load resistance.
 
  • #10
gneill said:
If you are unfamiliar with the Δ-Y transformations (It would be worth your while to look it up!), then an alternative is to apply a voltage source across AB and solve the circuit for the current that the source produces. Ohm's law will then tell you the effective load resistance.

Even if a voltage source is applied, wouldn't star-delta transformation be needed. I don't think there is any other way to find the currents.
Nodal analysis?
 
  • #11
upload_2017-12-15_7-45-5.png
 

Attachments

  • upload_2017-12-15_7-45-5.png
    upload_2017-12-15_7-45-5.png
    12.3 KB · Views: 574
  • #12
the four 9 ohm resistors (two in each series) can be replaced judiciously by two six ohm resistors and two 12 ohm resistors in series with two six ohm resistors. Then you have a symmetric circuit around the middle 12 ohm resistor. Because of symmetry, there is no reason to expect a different potential at either end of the middle 12 ohm resistor. Clever problem eh.?
 
  • #13
Babadag, there's no need to derive a mesh solution. Simple reduction by various parallel and series combinations gives 6 ohms.
 
  • #14
You are right. My mistake. The result is 6 indeed.:frown:
 
  • #15
I actually said 'remove it'.
yecko said:
but why no voltage across it?
If you look at the circuit, the left side of the 12 ##k\Omega## resistor is connected to the right sides of both 3 ##k\Omega## via the same resistances, hence it's voltage is an average of the corresponding nodes voltages. The same is true for the right side of that resistor.
And the final proof: you shorted it and got the correct answer. Now remove it and redo the calculations, you'll get exactly the same answer.

yecko said:
what do you mean by "delta" and "star"?
(i have never learned wheatstone bridge...)
Do you know the loop current method? you can use that too.
 
  • #16
jaus tail said:
Even if a voltage source is applied, wouldn't star-delta transformation be needed. I don't think there is any other way to find the currents.
Nodal analysis?
No, you can avoid star-delta if you apply mesh or nodal analysis, or even "raw" KVL and KCL equations with branch currents.
 
  • Like
Likes jaus tail
  • #17
mpresic2 said:
the four 9 ohm resistors (two in each series) can be replaced judiciously by two six ohm resistors and two 12 ohm resistors in series with two six ohm resistors. Then you have a symmetric circuit around the middle 12 ohm resistor. Because of symmetry, there is no reason to expect a different potential at either end of the middle 12 ohm resistor. Clever problem eh.?
I'm struggling to understand this. Can you please post a picture of the configuration?
 
  • #18
jaus tail said:
I'm struggling to understand this. Can you please post a picture of the configuration?
The 9kΩ resistors are arranged as a potential divider, setting their midpoint at (in this case) 50% of the potential across them all. The pair of 6kΩ resistors likewise form a similar potential divider ...
 
  • Like
Likes jaus tail

What is equivalent resistance?

Equivalent resistance is the combined resistance of multiple resistors in a circuit. It is the total resistance that the current experiences when flowing through the circuit.

How do I calculate equivalent resistance?

To calculate equivalent resistance, you can use the formula 1/Req = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn, where Req is the equivalent resistance and R1, R2, R3, etc. are the individual resistances in the circuit. Alternatively, you can use the parallel and series resistor rules to simplify the circuit and calculate the equivalent resistance.

What is the difference between series and parallel resistors?

Series resistors are connected end-to-end, so the current flowing through them is the same. The equivalent resistance of series resistors is the sum of individual resistances. Parallel resistors, on the other hand, are connected side-by-side, so the voltage across them is the same. The equivalent resistance of parallel resistors is calculated using the parallel resistor rule.

Why is equivalent resistance important?

Equivalent resistance is important because it helps us understand the behavior of a circuit. It allows us to calculate the current flowing through the circuit and the voltage across each resistor. It also helps us determine the power dissipated in the circuit and the efficiency of the circuit.

Can I use equivalent resistance for any type of circuit?

Equivalent resistance can be used for simple circuits with only resistors. However, for more complex circuits with other components like capacitors and inductors, the concept of equivalent impedance is used. Equivalent impedance takes into account the effects of all components in the circuit, not just resistors.

Similar threads

  • Engineering and Comp Sci Homework Help
Replies
11
Views
5K
  • Engineering and Comp Sci Homework Help
Replies
2
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
5
Views
3K
  • Engineering and Comp Sci Homework Help
Replies
8
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
17
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
6
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
8
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
10
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
17
Views
9K
  • Engineering and Comp Sci Homework Help
Replies
12
Views
2K
Back
Top