How Do I Calculate Equivalent Resistance in Complex Circuits?

[Decan]

Equivalent Resistance question HELP!

Homework Statement

The following diagram shows part of an electrical circuit. Find the equivalent resistance between points A and B of the resistor network.

Here is the circuit in question : http://img182.imageshack.us/img182/8742/physicsyf0.th.png

Homework Equations

R_s = R_1 + R_2 + R_n
R_p = (1/R_1 + 1/R_2 + 1/R_n)^-1

The Attempt at a Solution

I figured out the equations listed above...we have not discussed this in lecture yet (and the homework is due tomorrow before our recitation so I can't get help) so I tried the best I could by reading the text. Here's what I think...

The 28 ohm, 5 ohm, and 23 ohm resistors are in a series so they can be replaced by a 56 ohm resistor. The same can be said about the 38, 8, and 7 ohm resistors being replaced with a 73 ohm resistor. Now, the 9 ohm, the 73 ohm, and 56 ohm resistors are parallel so using the R_p equation:

R_p = (1/9 + 1/73 + 1/56)^-1 = 7.00 ohms

The correct answer is 8 ohms...what am I doing wrong? Do I not understand the concept of series and parallel circuits correctly? Thanks in advance to anyone who helps.

 

[berkeman]

You have the right idea, but as you collapse each combination of resistors into one resstor, keep that one resistance as you do further combinations.

-- combine 28 5 and 23 in series

-- combine that in parallel with 8

-- add that in series with 38 and 27

-- and then what do you do with the 9 Ohms?

 

[Decan]

Ah, I see...then the 9 ohm resistor would be parallel to the final resistor...thanks!