Identifiying Parallel And Series Connections

[anthonych414]

Homework Statement

I'm having a bit of a problem identifying series and parallel connections of resistors in some new circuits I've been exposed to, like the ones posted below. I'd be very grateful if anyone could give me some pointers or tips, or perhaps link me to some videos/explanations.

Homework Equations

The Attempt at a Solution

 

[phinds]

The definition of series and parallel is EXTREMELY simple:

Parallel: both ends of two resistors join each other

Series: One end of one resistor hooks to one end of another resistor and that junction does NOT hook to anything else.

 

[anthonych414]

The definition of series and parallel is EXTREMELY simple:

Parallel: both ends of two resistors join each other

Series: One end of one resistor hooks to one end of another resistor and that junction does NOT hook to anything else.

I know that definition but how can I apply it in the circuits attached above? Could you identify the series and parallel connections in those circuits and show the logic followed in that identification?

 

[mfb]

I know that definition but how can I apply it in the circuits attached above? Could you identify the series and parallel connections in those circuits

That depends on the points you are interested in. There is no parallel or series connection for all setups in this sketch.

An analysis of the resistance between a and b will look different from an analysis of the resistance between a and c, for example.

 

[anthonych414]

That depends on the points you are interested in. There is no parallel or series connection for all setups in this sketch.

An analysis of the resistance between a and b will look different from an analysis of the resistance between a and c, for example.

It's between a and b in both circuits. Can you explain how to find out which are in series and which are in parallel?

 

[gneill]

1) Don't be fooled by the drawn orientation of components; diagonal, horizontal, vertical --- makes no difference at all. The only thing that matters is what they connect to. That is to say, Topology counts, not artwork.
2) The same goes for wires: A wire that wiggles around the page and jumps over other things is theoretically the same as a point! What matters is what it connects together, and all those connections can be thought of as being to a single point.
3) You are free to rearrange the diagram in any way you want so long as you don't disturb the topology (what is connected to what). You can stretch or shrink wires, reorient components, slide connections along wires, etc., to your heart's content if it will make the circuit more obvious to you.

In your first circuit, which I've reproduced here:

Note the points I've marked C and D in red. There's no reason why that wire has to be that long. And there's no reason that those resistors connected to it have to have the connection points where they're shown. The same goes for the wire at the bottom and its connections.

Why don't you redraw the circuit, bringing the connections of those resistors to the center of those those wires? (Slide the connections of the 4 and 12 Ohm resistors to the middle of the wire CD. Do the same for the pair of resistors at the bottom with its wire. Can you spot any parallel or serial opportunities now?

For the second circuit, try to imagine what it would look like if your were to "pick up" node d and pull it over to lie between nodes a and b. Don't be afraid to bend and twist the wires or reorient the components. Just don't break any connections!

Note that not every circuit will present you with opportunities of parallel or series components to simplify, no matter how you rearrange the diagram. In those cases there are other methods you will have to apply, which I'm sure you'll be learning about soon.

 

[anthonych414]

1) Don't be fooled by the drawn orientation of components; diagonal, horizontal, vertical --- makes no difference at all. The only thing that matters is what they connect to. That is to say, Topology counts, not artwork.
2) The same goes for wires: A wire that wiggles around the page and jumps over other things is theoretically the same as a point! What matters is what it connects together, and all those connections can be thought of as being to a single point.
3) You are free to rearrange the diagram in any way you want so long as you don't disturb the topology (what is connected to what). You can stretch or shrink wires, reorient components, slide connections along wires, etc., to your heart's content if it will make the circuit more obvious to you.

In your first circuit, which I've reproduced here:

Note the points I've marked C and D in red. There's no reason why that wire has to be that long. And there's no reason that those resistors connected to it have to have the connection points where they're shown. The same goes for the wire at the bottom and its connections.

Why don't you redraw the circuit, bringing the connections of those resistors to the center of those those wires? (Slide the connections of the 4 and 12 Ohm resistors to the middle of the wire CD. Do the same for the pair of resistors at the bottom with its wire. Can you spot any parallel or serial opportunities now?

For the second circuit, try to imagine what it would look like if your were to "pick up" node d and pull it over to lie between nodes a and b. Don't be afraid to bend and twist the wires or reorient the components. Just don't break any connections!

Note that not every circuit will present you with opportunities of parallel or series components to simplify, no matter how you rearrange the diagram. In those cases there are other methods you will have to apply, which I'm sure you'll be learning about soon.

Okay, I've been solving problems and I'm starting to get the hang of it, thank you very much.