Hello Community...

I refer to Q40 from the worksheets on ''DC Series/Parallel circuits''.

http://www.allaboutcircuits.com/worksheets/series-parallel-dc-circuits/

Judging by the table of values, R3 and R4 are in series...ok, I get this.

But, R1 is deemed to be parallel to R3 <--> R4. Then, all this is in series with R2.

Could anyone please explain the reasoning behind this as I would have put R1 and R2 as parallel, which in turn is in series with R3 and R4 combined..??

Many thanks to all of you for reading/replying.

Wayne

 

These circuits are all equivalent. Follow the sequence of reductions...



Note the equivalence:

 

A simple way to tell if two components are in series is to place one index finger at opposite ends of one of the components. If you can move both fingers along wires and get both fingers to the opposite ends of another component, then those two components are in parallel.

 

Another technique is to color code the nodes:



Two components are in parallel if and only if the nodes they are connected two are the same color. This is because two components are in parallel if and only iff they have the same voltage applied to them. Since a node is considered to have the same voltage anywhere along it (is said to be "equipotential"), two components that share the same node are in parallel.

So R1 is connected to the red and the green node while R2 is connected to the yellow and the green node. Hence they are NOT in parallel.

To components are in series if the node connecting them ONLY connects them (and nothing else). So R2 and the battery are in series while R3 and R4 are in series. Any node that connects only two components means that those components are in series because whatever current enters one component MUST flow through the other component.

 

Another technique is to color code the nodes:

View attachment 87835

Two components are in parallel if and only if the nodes they are connected two are the same color. This is because two components are in parallel if and only iff they have the same voltage applied to them. Since a node is considered to have the same voltage anywhere along it (is said to be "equipotential"), two components that share the same node are in parallel.

So R1 is connected to the red and the green node while R2 is connected to the yellow and the green node. Hence they are NOT in parallel.

To components are in series if the node connecting them ONLY connects them (and nothing else). So R2 and the battery are in series while R3 and R4 are in series. Any node that connects only two components means that those components are in series because whatever current enters one component MUST flow through the other component.

Very helpful....many thanks

 

These circuits are all equivalent. Follow the sequence of reductions...

View attachment 87833

Note the equivalence:

View attachment 87834

Awesome....so much clearer now!!