What is the Equivalent Resistance between Points A and B in this Circuit?

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Homework Help Overview

The discussion revolves around finding the equivalent resistance between points A and B in a circuit involving resistors. The original poster states that the equivalent resistance is 27 Ohms and seeks to determine the value of an unknown resistance R.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the concept of equivalent resistance, with one suggesting to first find the equivalent resistance of resistors in parallel before combining them with a series resistor. Questions about the exact value of R and requests for showing work are also raised.

Discussion Status

Some participants have provided guidance on how to approach the problem, including steps to find equivalent resistance in parallel and series configurations. There is an ongoing exploration of the calculations involved, with no explicit consensus reached on the final value of R.

Contextual Notes

Participants are discussing the calculations based on a specific circuit diagram, which is not provided in the thread. There are indications of rounding in the values discussed, and the original poster expresses uncertainty about the initial steps in solving the problem.

Ballin27
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Homework Statement


The equivalent resistance between points A and B of the resistors shown in the figure is 27Ohms.

Find the value of resistance R.

Here is the diagram: http://session.masteringphysics.com/problemAsset/1122575/1/Walker.21.36.jpg

Homework Equations



Rseries = R1+R2+R3...

The Attempt at a Solution



Not really sure where to even start, having a real hard time with equivalent resistance. If someone could point me in the right direction it would be greatly appreciated.
 
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Hi Ballin27! :smile:

(have an ohm: Ω :wink:)
Ballin27 said:
Not really sure where to even start, having a real hard time with equivalent resistance. If someone could point me in the right direction it would be greatly appreciated.

The two on the right are in parallel, so find their equivalent resistance first.

Once you have that, the 12 Ω on the left is in series with it, so find the total equivalent resistance (which you can then put equal to 27 Ω) …

what do you get? :smile:
 
Thanks for the help tiny-tim! :biggrin:

I ended up getting 21 Ω which turned out to be right :D
 
Ballin27 said:
Thanks for the help tiny-tim! :biggrin:

I ended up getting 21 Ω which turned out to be right :D

Yes, that's the rounded value. What is the exact value?
Show us your work.
 
zgozvrm said:
Yes, that's the rounded value. What is the exact value?
Show us your work.

Here it is:

1/Req1 = 1/55 + 1/R = 1/55(R/R) + 1/R(55/55) = R/55R + 55/55R = (55+R)/55R

Req1= 55R/(55+R)

12 + 55R/(55+R) = 27
12 + 55R = 27(55+R)
55R = (27-12)(55+R)
55R = (15R) + (15 x 55)
40R = 825

R = 20.625
 
ballin27 said:
here it is:

1/req1 = 1/55 + 1/r = 1/55(r/r) + 1/r(55/55) = r/55r + 55/55r = (55+r)/55r

req1= 55r/(55+r)

12 + 55r/(55+r) = 27
12 + 55r = 27(55+r)
55r = (27-12)(55+r)
55r = (15r) + (15 x 55)
40r = 825

r = 20.625
perfect!
 

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