Equivalent resistance between two nodes homework

In summary, Jason suggested that the equivalent resistance between any two nodes in the circuit is the sum of the resistances of the individual nodes.
  • #1
JasonHathaway
115
0

Homework Statement



Determine the equivalent resistance Req as seen by the voltage source VS (the resistance between a and b)

http://i.imgur.com/A1ueQnd.jpg


Homework Equations



Series-Parallel combinations

The Attempt at a Solution



http://i.imgur.com/K1ItpF0.jpg

The only resistor that have both a and b on its terminals is R2 (12 ohms)

So, is Req=R2=12 ohms?
 
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  • #2
JasonHathaway said:

Homework Statement



Determine the equivalent resistance Req as seen by the voltage source VS (the resistance between a and b)

http://i.imgur.com/A1ueQnd.jpg


Homework Equations



Series-Parallel combinations

The Attempt at a Solution



http://i.imgur.com/K1ItpF0.jpg

The only resistor that have both a and b on its terminals is R2 (12 ohms)

So, is Req=R2=12 ohms?

Nope. There are other paths that current can take starting at a and ending at b. Start simplifying the easy parts first, working from the left side of the circuit.
 
  • #3
No. The Req is what you get if you resolve all the resistors (including R1) down to one new resistor.

For example if you were to measure the current going from the voltage source into node "a" and called that "Is" then..

Req = Vs/Is

edit: Sorry my post crossed with the one from gneil.
 
  • #4
Thank you gneil, CWatter for your quick responses

and it's better to hear (or read actually) as many opinions as possible

So basically what I am going to do is to find the equivalent resistance of all the resistors.

So the idea is to follow the current's path from a until it gets to b

but if I was asked to the find the equivalent resistance between f to e, the answer would be R2+R3+R4, isn't?
 
  • #5
JasonHathaway said:
Thank you gneil, CWatter for your quick responses

and it's better to hear (or read actually) as many opinions as possible

So basically what I am going to do is to find the equivalent resistance of all the resistors.

So the idea is to follow the current's path from a until it gets to b

but if I was asked to the find the equivalent resistance between f to e, the answer would be R2+R3+R4, isn't?

Your best strategy is to systematically combine resistors where series or parallel opportunities arise, reducing the circuit complexity as you go. So yes, you could reduce R2, R3, and R4 to a single resistance value, replacing the three with a single resistor that is their sum.

Your original diagram did not include labels e and f, but I presume you meant something like this:

attachment.php?attachmentid=66384&stc=1&d=1391798952.gif


So imagining that the circuit was severed at those points, the equivalent resistance seen "looking into" those terminals to the left would be Req = R2 + R3 + R4.
 

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  • #6
gneill said:
Your original diagram did not include labels e and f,

He's referring to e and f in his solution attempt:

http://i.imgur.com/K1ItpF0.jpg

The OP is really struggling with this; he's had help in another forum:

http://forum.allaboutcircuits.com/showthread.php?t=94166

Jason, the equivalent resistance seen between ANY two nodes in this circuit will include the effect of ALL the resistors in the entire circuit.

The Req between a and b is not just the value of R1. The Req between e and f is not just R2+R3+R4; it involves ALL the resistors in the circuit.

Imagine that you replace R2, R3 and R4 with a single resistor (call that single resistor Rx); what would be the value of that resistor? Now Rx is in parallel with R5; you could replace the parallel combination of Rx and R5 with another equivalent resistor (call it Ry).

Ry is now in series with R6 and that series combination could be replaced with an equivalent resistor (call it Rz). Now Rz is in parallel with R8; replace that with another equivalent resistor (call it Ra). Ra is now in series with R7, which can be replaced with an equivalent resistor (call it Rb). Rb is in parallel with R1, and that is your answer.
 
  • #7
You got me :P

It's true, I'm really really struggling with this, but I guess I'm getting the point.

As long as the current flows through a resistor, it should be considered when calculating Req.

Thank you, everyone :)
 
  • #8
Before you go away, try the calculation I described and post your result. We really want to help you and if you get the right answer, we'll feel like we were a help. If you don't, we can help you with your stumbling block.
 
  • #9
OK, where R1=12, R2=15, R3=25, R4=25, R5=30, R6=7, R7=4, R8=15

The total resistance would be equal to 6.42 ohms?
 
  • #10
If I solve with exact rational arithmetic, I get Req = 132924/20773 = 6.39888

I suspect you did everything correctly, but probably didn't carry enough digits in your calculations.

Congratulations!
 
  • #11
wheeew (A long long one)

Thank you for your concerning :)
 

FAQ: Equivalent resistance between two nodes homework

1. What is equivalent resistance between two nodes?

The equivalent resistance between two nodes is the overall resistance that is seen between those two nodes in a circuit. It takes into account all the resistors and their respective values that are connected between those two nodes.

2. How is equivalent resistance calculated?

To calculate equivalent resistance, you need to first identify all the resistors connected between the two nodes. Then, use the following formula: 1/Req = 1/R1 + 1/R2 + ... + 1/Rn, where Req is the equivalent resistance and R1, R2, etc. are the individual resistors. Finally, take the reciprocal of the result to get the equivalent resistance.

3. Why is equivalent resistance important?

Equivalent resistance is important because it helps in simplifying complex circuits. It allows us to replace multiple resistors with a single resistor that has the same effect on the circuit. This makes circuit analysis and calculations easier.

4. Does equivalent resistance change in series and parallel circuits?

Yes, equivalent resistance changes in series and parallel circuits. In series circuits, equivalent resistance is the sum of all the resistors, while in parallel circuits, it is calculated using the formula: Req = (R1 x R2) / (R1 + R2). This means that equivalent resistance in parallel circuits is always less than the smallest individual resistor.

5. How is equivalent resistance affected by the arrangement of resistors in a circuit?

The arrangement of resistors in a circuit can affect the equivalent resistance. In series circuits, adding more resistors increases the equivalent resistance, while in parallel circuits, adding more resistors decreases the equivalent resistance. Changing the order of resistors in a circuit also changes the equivalent resistance, but the overall value remains the same.

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