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

[Ballin27]

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.

 

[tiny-tim]

Hi Ballin27!

(have an ohm: Ω )

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? ​

 

[Ballin27]

Thanks for the help tiny-tim!

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

 

[zgozvrm]

Thanks for the help tiny-tim!

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.

 

[Ballin27]

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

 

[zgozvrm]

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!