Resistors - connected in series or in parallel

[kandrew]

Resistors -- connected in series or in parallel

Homework Statement

The problem is asking for the currents, but I have a question about the resistors. I've been having trouble determining whether resistors are connected in series or in parallel. I've already looked at another thread in this forum about resistors, but it did not help with this situation. The circuit below is very basic, but I think it would help with more advanced circuitry if I knew about these resistors.

Homework Equations

NA

The Attempt at a Solution

I know:
• the 40Ω and 20Ω are connected in series, and
• the 125Ω and 50Ω are connected in parallel.

I'm curious as to whether the 240Ω and the 60Ω (equivalent of 40Ω and 20Ω) are also connected in parallel with the 125Ω and 50Ω. And I'd like to know if there are any other resistor connections that can be simplified, or is that 2Ω just a loner?

 

[gneill]

Homework Statement

The problem is asking for the currents, but I have a question about the resistors. I've been having trouble determining whether resistors are connected in series or in parallel. I've already looked at another thread in this forum about resistors, but it did not help with this situation. The circuit below is very basic, but I think it would help with more advanced circuitry if I knew about these resistors.

Homework Equations

NA

The Attempt at a Solution

I know:
• the 40Ω and 20Ω are connected in series, and
• the 125Ω and 50Ω are connected in parallel.

I'm curious as to whether the 240Ω and the 60Ω (equivalent of 40Ω and 20Ω) are also connected in parallel with the 125Ω and 50Ω. And I'd like to know if there are any other resistor connections that can be simplified, or is that 2Ω just a loner?

Get yourself a whack of scrap paper or a whiteboard, and each time you combine resistors (series or parallel) redraw the circuit replacing the combined resistors with a single resistor. That should help you to see new series/parallel opportunities as you go.

If you are reducing the circuit from right to left (so, starting with the series combination of the 40 and 20 Ohm resistors that you mentioned), clearly the 2Ω resistor will eventually be in series with the "result" of the reduction of the 240-40-20 Ohm cluster. Do the reductions step by step and you'll see.

 

[NascentOxygen]

I'm curious as to whether the 240Ω and the 60Ω (equivalent of 40Ω and 20Ω) are also connected in parallel with the 125Ω and 50Ω. And I'd like to know if there are any other resistor connections that can be simplified, or is that 2Ω just a loner?

It often is clearer if you think in terms of parallel and series paths. If you can find a route that allows current to flow from one end of a resistor to the [node at the] other end of that resistor, and without passing through that resistor, you have found a parallel path.

If all current that passes through a particular resistor must also pass through another resistor, there being no alternative route, then those two resistors are in series.

As far as the 50Ω is concerned, the 240Ω and the 60Ω form part of a parallel path, but they alone don't comprise that path, there is the 2Ω in series with them.

 

[CWatters]

Get yourself a whack of scrap paper or a whiteboard, and each time you combine resistors (series or parallel) redraw the circuit replacing the combined resistors with a single resistor.

This suggestion gets my vote. Should make things very obvious for you.

 

[rezeew]

In this circuit, the 240Ω and 60Ω resistors are connected in parallel with the 125Ω and 50Ω resistors. This can be determined by looking at the connections between the resistors. In a parallel circuit, the resistors are connected at both ends, while in a series circuit, the resistors are connected in a line. Since the 240Ω and 60Ω resistors are connected at both ends with the 125Ω and 50Ω resistors, they are in parallel. The 2Ω resistor is a "loner" and does not affect the rest of the circuit, as it is not connected in series or parallel with any other resistors. It is important to understand the connections between resistors in a circuit in order to accurately determine the equivalent resistance and current flow.