How to Distinguish Resistors in Series vs. in Parallel

[minimario]

How do you tell if 2 resistors (or capacitors, etc.) are in parallel or in series?

For example, calculate the resistance in the following circuits:

How is the first circuit simplified, and what is an easy way to distinguish which resistors are in series, and which are in parallel?

Thanks!

 

[mfb]

If both sides are connected with each other each, they are in parallel.
If they are in series (---RRR--RRR--) and no other part is connected to the cable in between, they are in series.

There are networks where none of those two rules can be used to simplify anything, but then you can use more powerful tools to handle those (Kirchhoff's laws).

 

[minimario]

If both sides are connected with each other each, they are in parallel.
If they are in series (---RRR--RRR--) and no other part is connected to the cable in between, they are in series.

There are networks where none of those two rules can be used to simplify anything, but then you can use more powerful tools to handle those (Kirchhoff's laws).

In the first example, the solution says to first connect the 20 and 5 Ohm resistors (which are in series), then connect the resulting 25 Ohm to the bottom 10 Ohm and 5 Ohm resistor, these 3 in parallel. Can you explain why these 3 are in parallel?

Thanks!

 

[berkeman]

In the first example, the solution says to first connect the 20 and 5 Ohm resistors (which are in series), then connect the resulting 25 Ohm to the bottom 10 Ohm and 5 Ohm resistor, these 3 in parallel. Can you explain why these 3 are in parallel?

Thanks!

Because they are each connected to the same 2 nodes.

 

[berkeman]

Also, do you see why the 10 Ohm resistor that is in series with the voltage source is *not* in parallel with those other resistors?

 

[Philip Wood]

The 5 ohm and the 20 ohm at the sides are clearly in series with each other, making 25 ohm. This 25 ohm is in parallel with the bottom 5 ohm and the middle 10 ohm. This parallel combination is in series with the top 10 ohm.

I don't think there's a routine for doing this sort of thing. You just see it. It comes with practice.

Note that there are arrangements of resistors which can't be analysed into series and parallel combinations. It's probably safe to assume that your teachers and textbooks won't give them to you at this stage!

 

[minimario]

Also, do you see why the 10 Ohm resistor that is in series with the voltage source is *not* in parallel with those other resistors?

No, that is what I am asking about.

 

[berkeman]

No, that is what I am asking about.

Are both ends of the resistor that is in series with the voltage source connected to the same nodes as the other resistors that are in parallel? If not, what is in the way...? :-)

 

[minimario]

Why are the left 5 ohm, middle 10 ohm, and right 20 ohm not in series?

 

[berkeman]

Why are the left 5 ohm, middle 10 ohm, and right 20 ohm not in series?

Because the middle 10 Ohm resistor is not 10 Ohms, it is 10//5 Ohms...

 

[minimario]

What are you saying?

 

[berkeman]

How do you tell if 2 resistors (or capacitors, etc.) are in parallel or in series?

For example, calculate the resistance in the following circuits:

How is the first circuit simplified, and what is an easy way to distinguish which resistors are in series, and which are in parallel?

Thanks!

What are you saying?

I'm saying that if you want to combine the bottom resistors, that middle effective resistance is not 10 Ohms. It is 10 Ohms in parallel with the 5 Ohm resistor right below it. It would be a mistake to try to combine the left 5, middle 10 and right 20 Ohm resistors in series, because the middle resistance is *not* 10 Ohms. Having the 5 Ohm resistor in parallel with it lowers the resistance to 10//5 Ohms.

And after you combine the 10//5 Ohm middle resistors, you would combine the 5+20 Ohm resistors on the outside branch in series. And then you are left with two resistances that you can combine in parallel, since they are both connected to the same 2 nodes.

 

[mfb]

Why are the left 5 ohm, middle 10 ohm, and right 20 ohm not in series?

There are other parts connected in between.