# Problem 4.101

Discussion in 'Homework Help' started by sunnysun, Jun 15, 2013.

1. ### sunnysun Thread Starter New Member

Jun 15, 2013
6
0
Hey guys, I just wanna ask you about problem 4.101 in Electric Circuits 9e by Nilsson and Riedel. I'm confused on how to simplify the two pairs of parallel resistors (1Ω||3Ω and 2Ω||4Ω). How should I connect the equivalent resistors? What should I do with the wire between them? Please explain it to me as clearly as you can. Sorry if I can't provide you an image of the problem. Thank you in advance.

2. ### gootee Senior Member

Apr 24, 2007
447
51
If I understand your question, you replace each parallel pair with a single resistor. After that, there is no wire between them, since there is no "them", because one resistor has replaced them. Its connections are to the same two points that both of the resistors in the parallel pair were connected to, originally.

Not sure what "wire between them" you reference. Topologically, a wire is all the same single point, in an ideal circuit.

You replace each parallel pair with a single resistor. Replace the wire(s) that were connecting the corresponding ends of two resistors together with the single wire from the end of the resistor that replaces that parallel pair. i.e. The single equivalent resistor connects to the same two places that the original parallel pair was connected.

Are any of the remaining single resistors now in parallel with each other? If so, replace them with a single equivalent resistor, in the same way as before.

In case there are also series resistors, you can sum their resistances and replace them with a single resistor with their summed value.

sunnysun likes this.
3. ### sunnysun Thread Starter New Member

Jun 15, 2013
6
0
Oh, thank you for your answer. It really helped a lot. I can solve the problem now. By the way, I was referring to the blank diagonal wire with no resistor that connects the two pairs of parallel resistor.

4. ### JoeJester AAC Fanatic!

Apr 26, 2005
3,909
1,738
Post the schematic of the circuit.

5. ### WBahn Moderator

Mar 31, 2012
23,093
6,945
You cause little but confusion when you assume that just by giving a problem number in a particular book that anyone here actually has that book (and that specific edition of that book).

The least you should do is scribble something together in Paint. Doesn't have to be fancy. Remember, you are asking strangers to spend their time trying to help you, the least you can do is spend some of your time making it easier for them to do so.

As it turns out, I do happen to have that text. The two sets of resistors you refer to are, indeed, in parallel (not something that we can just take for granted given how often we see people say that something is in parallel with something or in series with something else and, in fact, they aren't and that doesn't become apparent until they finally post a schematic).

On thing that you have to be careful here is to maintain the integrity of the voltage across the 2Ω resistor since that voltage is the controlling voltage for a dependent current source.

6. ### sunnysun Thread Starter New Member

Jun 15, 2013
6
0
Sorry guys for not posting the schematic diagram because I wasn't finished remapping my mac keyboard but now I'm done so I can use printscreen now. Here it is:

All I want to know is what happens to the red wire if I replaced the parallel resistors with their equivalent resistors (1Ω||3Ω = (3/4)Ω, 2Ω||4Ω = (4/3)Ω) and where should I connect the equivalent resistors?

7. ### WBahn Moderator

Mar 31, 2012
23,093
6,945
The red wire (and the wire fragments connecting the red wire to the four resistors) are all simply one, single, node.

Imagine grabbing the connection dot at the upper-left end of the red wire and sliding it down the red wire (with the red wire getting shorter and shorter). As you do this, the 2Ω resistor rotates steadily clockwise and the 1Ω resistor rotates steadily counter clockwise. Keep moving it until the red wire is just this tiny little wire and the two connection dots at each end are very close to each other.

The attached modified picture shows the idea.

Do you see how you can make the red line simply go away, leaving the two sets of resistors in clear parallel pairs?

The key to remember is that the lines on a schematic represent connectivity (in almost all cases -- there are exceptions, but those should be clearly identified). As long as the connectivity is maintained, it doesn't matter how you draw the components and the wires.

• ###### httpimg836_imageshack_usimg83621093s2.png
File size:
20.5 KB
Views:
49
sunnysun likes this.
8. ### sunnysun Thread Starter New Member

Jun 15, 2013
6
0
Great explanation! Thank you WBahn I can proceed in solving the problem. The confusion is gone. Thank you very much.