Adding Up Resistors: Order of Operations Explained

[prettykitty]

I have added an attachment of the circuit for clarity.

I initially began by assuming that the 13 ohm and 24 ohm resistors were in parallel and I got the Req for them. Then since the top resistor seemed to be in series with them I added its value. This is wrong of course, the correct sequence of steps is:

Treat the top resistor and the 13 ohm resistor as as if they are in series. Then with the attained Req add the 24 ohm resistor using the correct math for parallel resistors.

Where did my thinking originally go wrong?
My guess is that it has something to do with some sort of "order of operations" for circuits. Can that be clarified please?

 

[lewando]

The 13-ohm and 24-ohm are simply, definitionally, not in parallel.

 

[prettykitty]

Yes great, I knew that already.
Can you be a little more helpful and explain why?
Statements of fact are of little help.

 

[lewando]

Sorry, I was just pointing out where your thinking originally went wrong.

By definitionally, I mean that thinking that the resistors (13 and 24-ohm) are in parallel violates the definition of "in parallel", which is: two elements are considered "in parallel" if they share common starting and ending nodes, which those two elements do not.

The top resistor and the 13-ohm are definitionally "in series" (connected end-to-end with no branching node in between).

 

[prettykitty]

Hey no problem, thanks a bunch!