# Equivalent resistance between a and b -- Complex circuit

• kamhogo
In summary, the conversation discusses the concept of equivalent resistance and how to simplify a circuit by combining resistors in series and parallel. The mistake of leaving out a connection in a re-drawing is pointed out, and the use of a short circuit (0 ohm resistance) is explained. The conversation also touches on the concept of short circuits and how they affect the flow of electrons in a circuit. The conclusion is that a short circuit can be treated as a null resistor and can be left out of calculations.
kamhogo

## Homework Equations

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

## 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

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.

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

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

NascentOxygen said:
In the original image you can see there is a piece of wire parallel to the 10 ohm resistor ...
Should I add a "dummy" 0 ohm resistor on that piece of wire...? Would it change anything?

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

NascentOxygen said:
The 0Ω is across the 10Ω, a parallel resistance of 0Ω.
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?

kamhogo said:
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?
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?

NascentOxygen said:
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?

kamhogo said:
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...

NascentOxygen said:
It would read 0Ω, the wire is a short circuit

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

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

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

kamhogo said:
Ooooh. So the ideal 0 ohm wire would kind of force the 10 ohm resistor to be null? How does that work?
0 ohm in parallel with 10 ohm gives an equivalent resistance of 0 ohm between the two points.

NascentOxygen said:
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...
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?

kamhogo said:
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?
Thanks everyone for your mentoring! Appreciated from the bottom of my heart!

kamhogo said:
Does it mean that the 10 ohms resistor might as well not be there?
Yes.

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

kamhogo said:
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?

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.

kamhogo
NascentOxygen said:
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?
Second option! Thanks a lot for the image.

## 1. What is equivalent resistance in a complex circuit?

Equivalent resistance is the single resistance value that can replace a complex circuit without changing the overall current or voltage. It is calculated by combining all the individual resistances in the circuit using Ohm's law.

## 2. How do you calculate equivalent resistance in a complex circuit?

To calculate equivalent resistance, first identify all the individual resistances in the circuit. Then, use Ohm's law (R = V/I) to find the individual currents and voltages. Finally, use the formula Req = Vtotal/Itotal to calculate the equivalent resistance.

## 3. Is equivalent resistance the same as total resistance?

No, equivalent resistance and total resistance are not the same. Total resistance refers to the sum of all the individual resistances in a circuit, whereas equivalent resistance refers to the single resistance value that can replace the entire complex circuit.

## 4. Why is equivalent resistance important?

Equivalent resistance is important because it allows us to simplify complex circuits and make calculations easier. It also helps us understand the overall behavior of a circuit and predict how changes in resistance will affect the circuit.

## 5. Can the equivalent resistance ever be lower than the lowest individual resistance in a circuit?

No, the equivalent resistance can never be lower than the lowest individual resistance in a circuit. This is because adding more resistors to a circuit will always increase the overall resistance, and the equivalent resistance is the value that combines all the individual resistances in the circuit.

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