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

AI Thread Summary
The equivalent resistance between points A and B in the circuit is determined to be 27 Ohms. The problem involves finding the unknown resistance R, with the initial approach focusing on the parallel resistors on the right side of the circuit. After calculating the equivalent resistance of these resistors and combining it with the 12 Ohm resistor in series, the correct value for R was found to be approximately 20.625 Ohms. The calculations were verified through a series of equations, leading to the final result. This discussion highlights the process of solving for equivalent resistance in a mixed resistor circuit.
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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