Need help finding equivalent resistance in a circuit.

In summary: The equivalent resistance between A and B is 16.8 kΩ.In summary, To solve this problem involving delta wye transformations, it is helpful to treat the 3 kΩ resistors as 6 kΩ resistors in parallel. Then, the two sets of parallel resistors can be treated as parallel to each other and equivalent to 4.8 kΩ. Finally, the 4.8 kΩ resistor can be treated in series with the other four 3 kΩ resistors to obtain a final answer of 16.8 kΩ as the equivalent resistance between points A and B. It is important to remember to keep the A node in the circuit when finding the resistance between A
  • #1
naivy
40
0

Homework Statement



nTqaP.png


Homework Equations



delta wye transformations?

The Attempt at a Solution



PM9Qm.png

I feel like I should do delta wye transforms here, but that doesn't really lead me anywhere. Am I missing how I should do the problem?
 
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  • #2
Perhaps if you treated the two pairs of 3 kΩ resistors as two 6 kΩ resistors, you would realize the next step.
 
  • #3
Oh, wait... treat them as 6 kΩ resistors and then they become resistors in parallel?

In that case, does the whole half above A become equivalent to 4.8 kΩ? If so, then the whole circuit would have an equivalent resistance of 14.4 kΩ? Is that right? Or did I take your hint the wrong way...
 
  • #4
Your thinking and answer was wrong.

What is each 6 kΩ in parallel with?

Where is A?
 
  • #5
So I figured the following:

wQWD1.png


Treat the boxed resistors as 6 kΩ and then treat those to be in parallel with the 4 kΩ resistors under them.

Then we can treat the two pieces on the top (the two sets of parallel resistors) to be parallel with each other and be equivalent to 4.8 kΩ.

The region I'm thinking of as being equivalent to 4.8 kΩ is shown in the circle below.

QcQkN.png


Then, we can just treat the 4.8 kΩ to be in series with the other four 3 kΩ resistors to get an answer of (4.8 kΩ + 12 kΩ) 16.8 kΩ.

Can you please guide me as to where I messed up? Thank you so much for your help!
 
  • #6
You're supposed to be finding the resistance between A and B. You have to keep the A node!
 
  • #7
BGHCy.jpg
 
  • #8
That's correct.
 

FAQ: Need help finding equivalent resistance in a circuit.

How do I calculate equivalent resistance in a circuit?

Equivalent resistance can be calculated using the formula: Req = R1 + R2 + R3 + ..., where R1, R2, R3, etc. are the individual resistances in the circuit.

What is the purpose of finding equivalent resistance?

Finding equivalent resistance allows us to simplify complex circuits into a single resistor, making it easier to analyze and understand the behavior of the circuit.

Can equivalent resistance be greater than the individual resistances?

Yes, it is possible for the equivalent resistance to be greater than the individual resistances. This can happen when resistors are connected in series, where the equivalent resistance is the sum of all the resistors.

How do I find equivalent resistance in a parallel circuit?

In a parallel circuit, the formula for equivalent resistance is: 1/Req = 1/R1 + 1/R2 + 1/R3 + ... . To find the equivalent resistance, you would first find the reciprocal of each individual resistance, then add them together and take the reciprocal of the sum.

Can I use Kirchhoff's Laws to find equivalent resistance?

Yes, Kirchhoff's Laws - specifically, the Junction Rule and the Loop Rule - can be used to find equivalent resistance in a circuit. These laws are based on the principle of conservation of energy and can be used to solve for unknown variables in a circuit.

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