Series/Parallel Circuit: Identifying Resistor Placement

[Leslie]

How do you know if a resistor is in series or parallel in a series/parallel circuit?

 

[quantumdude]

Hi, and welcome to Physics Forums.

Two resistors are in series if the current leaving the first resistor is undivided by branching before entering the second resistor. That is, you should be able to draw a line on the circuit diagram from one resistor to the other without hitting a point at which the current branches off.

Two resistors are in parallel if the current that enters each resistor flows from the same node or source without passing through any other elements and if the current that leaves each resistor flows to the same node or sink without passing through any other elements.

See your textbook for illustrations.

edit: fixed an omission

 

[Gza]

The way that's always helped me think of a parallel configuration of resistors is that of both having the same potential difference across them.

 

[JohnDubYa]

I think the last explanation puts the cart before the horse.

Here is a simple explanation. If the current that travels through one resistor must flow through another resistor, the two resistors are in series.

If current has a choice between going through one resistor or another, then the two are in parallel.

 

[Gokul43201]

Additionally,

If you have resistors in series, the total resistance is greater than anyone of the resistances.

If you have resistors in parallel, the total resistance is smaller than the smallest of the resistances.

$$R(series)=R_1 + R_2 + R_3 +...$$

$$R(parallel)=[1/R_1 + 1/R_2 + 1/R_3 +...]^{-1}$$

 

[robphy]

I think of it this way.

Series: one terminal of R1 meets only one terminal of R2 (and no other element at that junction)

$$\begin{verbatim}<br /> ---R1---+---R2---<br /> \end{verbatim}$$

Parallel: corresponding terminals of R1 and R2 meet

$$\begin{verbatim}<br /> ---R1--- <br /> \end{verbatim}\begin{verbatim}<br /> ---+ +--- \end{verbatim}<br /> \begin{verbatim}<br /> ---R2---\end{verbatim}$$