# Equivalent resistance between a and b -- Complex circuit

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1. Apr 1, 2016

### kamhogo

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

2. Relevant equations
Req = [ ( 1 / R1) + ( 1 / R2) +. ....]^-1 (Parallel)
Req = R1 + R2 +. . . (Series )

3. The attempt at a solution
I tried to simplify the circuit by spreading it out but I guess something is wrong with my simplification since I can't arrive at the correct answer (7 ohms)....Can someone please point me in the right direction?h

2. Apr 1, 2016

### phyzguy

You're taking the right approach, you just made a mistake. Look at the 10 Ohm resistor in the original drawing and in your first re-drawing. It is not just in series with the last 3 Ohm resistor, there is an extra connection that you left out of your re-drawing. Try doing the simplification again.

3. Apr 1, 2016

### kamhogo

Is this better? My answer is still a little off though...

4. Apr 1, 2016

### Staff: Mentor

In the original image you can see there is a piece of wire parallel to the 10 ohm resistor ....

5. Apr 1, 2016

### kamhogo

Should I add a "dummy" 0 ohm resistor on that piece of wire...? Would it change anything?

6. Apr 2, 2016

### Staff: Mentor

The 0Ω is across the 10Ω, a parallel resistance of 0Ω.

7. Apr 2, 2016

### kamhogo

But then I'd have to compute [(1/0)+(1/10) ]^-1....and 1/0 is undefined....or do I just leave it out of the calculation?

8. Apr 2, 2016

### Staff: Mentor

I see.

It's 0/0 that is undefined; 1/0 is very large, infinity.

How about just thinking about it: what would a resistance meter measure if you had it connected to a 10Ω resistor and then you held a piece of thick wire across the resistor?

9. Apr 2, 2016

### kamhogo

10. Apr 2, 2016

### Staff: Mentor

It would read 0Ω, the wire is a short circuit.

If you had trouble using 0 in your computations, try instead a very small resistance, say 0.00001Ω and see where the calculations are heading....

11. Apr 2, 2016

### kamhogo

Please tell me more about short circuits. I haven't learned that yet....

12. Apr 2, 2016

### Staff: Mentor

A short circuit is a piece of wire (a perfect conductor, ideally) that joins one node to another and causes all points along it to have the same voltage.

13. Apr 2, 2016

### kamhogo

Ooooh. So the ideal 0 ohm wire would kind of force the 10 ohm resistor to be null? How does that work?

14. Apr 2, 2016

### cnh1995

0 ohm in parallel with 10 ohm gives an equivalent resistance of 0 ohm between the two points.

15. Apr 2, 2016

### kamhogo

I just tried the computation with 0.0001 ohm resistor in parallel with a 10 ohm resistor and I got 0. Wow! How can that be possible? Does it mean that the 10 ohms resistor might as well not be there????

16. Apr 2, 2016

### kamhogo

Thanks everyone for your mentoring!!!! Appreciated from the bottom of my heart!

17. Apr 2, 2016

### cnh1995

Yes.

18. Apr 3, 2016

### Staff: Mentor

If you were an electron in a circuit and were given the choice, would you prefer to fight your way through a 10Ω resistance, or glide almost effortlessly along a copper conductor?

19. Apr 3, 2016

### epenguin

Yes. In future you can just recognise it, and just forget any resistor in a position that is short-circuited like that, eliminate it and not include it in your calculation.

20. Apr 3, 2016

### kamhogo

Second option! Thanks a lot for the image.