# Homework Help: Finding the total resistance of a complex combination

1. Mar 11, 2012

### hms.tech

b]1. The problem statement, all variables and given/known data[/b]

Find the total resistance of this complex combination of resistors.
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2. Relevant equations

R(total)= (Rr)/(R+r)

3. The attempt at a solution

resistance of r(2) and r(3) = 20Ω
resistance of the combination of r(1) and the resultant 20 Ω(ie r(2) and r(3) ) = 20/3
resistance of r(3) and r(5) = 20Ω
resistance of te combination of r(4) and the resultant 20 (ie r(3) and r(5) ) = 20/3

I can't deduce and answer from the above (correct) results.

Need urgent Help !!

2. Mar 11, 2012

### tiny-tim

hi hms.tech!

have you tried using Kirchhoff's rules?

3. Mar 11, 2012

### hms.tech

No!
Would you kindly guide me how and where do we apply them in this situation.

(i know what they are but am confused about thier appropriate application in this design of resistors)

4. Mar 11, 2012

### tiny-tim

hi hms.tech!
just label the currents I1 I2 I3 I4 and I6 (with arrows of course!), do KVL and KCL, then find the total voltage drop between A and B, and divide by I6

what do you get?

5. Mar 12, 2012

### hms.tech

as i said, i am confused about the way to apply these laws in this unusual situatuion
your 2nd answer did not help any more than the first one (@tiny tim).

Kind Sir, will elaborate on the proposed method.
to put it simply, i am unable to find the voltage drop between A and B.

6. Mar 12, 2012

### Staff: Mentor

Stick either a voltage source or a current source at terminals AB. If it's a current source, find the voltage drop across AB. If it's a voltage source, find the current it's driving into the circuit. Either way the overall resistance of the circuit will be the ratio of the voltage to the current that the source delivers.

7. Mar 12, 2012

### Drao92

http://en.wikipedia.org/wiki/Y-Δ_transform
This is how you gona solve it.
1,2 and 3 are in triangle, same 3,4,5, change one combination with triangle-star transform and its solved.
My result is 10 ohm.
With kirchhoff.
Lets make I6=10 (you can give it any value you want)
Now, when the current is at A it will be divided by 2, because R1=R2, I3=0 from KCL.
So I1=5, I2=5, i4=5, i5=5.
Now, what you gona do its to KVL in loop 1 (yellow) to find Uab.
After finding Uab, Rab=Uab/I6.
https://www.physicsforums.com/attachment.php?attachmentid=45015&stc=1&d=1331595516

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Last edited: Mar 12, 2012
8. Mar 12, 2012

### SammyS

Staff Emeritus
This circuit can be analyzed by the use of symmetry.

An equivalent circuit to this is on with A at one corner of a square, and B at the opposite corner.

Label the other two corners C & D respectively, the corners being labeled: A, C, B, and D in a clockwise sense.
Resistor 1 connects corners A and C.

Resistor 2 connects corners A and D.

Resistor 5 connects corners C and B.

Resistor 4 connects corners D and B.

Resistor 3 connects corners D and C.​