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Question about resistor networks in the Electronics Demystified book

acidblue

Jul 11, 2012
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Having a problem calculating total R in a parallel resistor network.
On pages 28-29 , question 2-5 in particular, I don't see how the book is coming to
those answers.
According to my calculations on question 2 the answer is not 20 ohms as stated in
the book, I must be doing something wrong, but I can't figure it out.

This is how I'm doing it for question #2
there are 3 sets of 10, 20 and 30 ohm resistors in the network, so..
G= 1/R
R = 1/G
1/10 + 1/20 + 1/30 GIVES >> .1 + .05 + .033 = 0.1833 1/.1833 = 5.455 for the first set of three.
So I do 3 * 5.455 = 16.366

Which is wrong, the book says the answer is 20 ohms.
I don't see how they came up with 20 ohms??
What am I doing wrong?? Should I not be multiplying by 3??
 
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poor mystic

Apr 8, 2011
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:) Hi-
would you mind posting a circuit diagram describing the question, please?
 

(*steve*)

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I'd need to see the way they're connected to be able to tell you what you've done wrong, but essentially you're using the right approach.

for series resistors sum the resistances, for parallel resistors sum the conductances.

Remember to convert back to resistance if you're working in conductance.

So, if we had a 10R, 20R, and 30R in parallel the final resistance R would be:

1/R = 1/10 + 1/20 + 1/30
1/R = 0.1 + 0.05 + 0.0333333
1/R = 0.18333333
R = 5.45 ohms

I expect the circuit shows three 10 ohm resistors in parallel, in series with three 20 ohm resistors in parallel, in series with three 30 ohm resistors in parallel.

To solve that, you need to calculate the value of three 10 ohm resistors in parallel, add that to the value of three 20 ohm resistors in parallel, and then add that to the value of three 30 ohm resistors in parallel.

I also assume you're aware of how to quickly calculate the value of n resistors of the same value in parallel?

With a bit of thought, and if the problem is as I suspect it is, you can solve it by inspection (i.e. no calculations)
 

(*steve*)

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OK, so first calculate the value of the resistors in series, then do the resistors in parallel calculation (you should be able to do it by inspection once you've done the calculation and seen the simple relationship.
 

john monks

Mar 9, 2012
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I can clearly see that your confusion is not with the math but the concept of resistors in series so let's stand back from the math and just look at the circuit. You have an emf of 6 volts on a series string of resistors 10 ohms, 20 ohms, and 30 ohms. This represents the opposition to the flow of electrons and physics shows us that series resistances add up. Remember that. So you can tell how much the total resistance is of that string. Do not pay any attention to the other strings. They are irrelevant to the first questions. The current going through the 10 ohm resistor is the same as the current going through the other two resistors because the current has only one path. You know the voltage across the total string, 6 volts. You know the total resistance of the first string, you simply add them up because physics show us that they add up. Physics also show us that the current traveling through a resistance is directly proportional to the voltage across the resistance. For example 1 volt across a 1 ohm resistor results in 1 amp traveling through the resistor. Now you have enough information to solve for the current traveling through the 10 ohm resistor. The formulas you show are correct but you are being confused by them. You must first understand the physics, that is the science of resistance, voltage, and current, and then apply the proper definitions of voltage, amperage, and ohms to figure out the problem. Bottom line is you should not apply a formula that you cannot derive from science and definitions. A formula may work for this problem but when the circuit changes you will be stuck all over again.
 

Laplace

Apr 4, 2010
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1/10 + 1/20 + 1/30 GIVES >> ...
What am I doing wrong??

The first thing you are doing wrong is treating the 10+20+30 ohm resistors as though they are in parallel instead of in series.
 
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acidblue

Jul 11, 2012
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OK I'm so confused right now.
Treating them as series resistors doesn't give the correct answer.

R1+R2+R3= 10+20+30 =60, since there are 3 rows, 3*60 = 180 so 1/180 =0.0555
OR should it be 1((1/30+1/60+1/90)) = .033+.0166+.0111 = .0607 so 1/.0607 = 16.47
Which isn't correct either.

This is driving me nuts, I don't see how you can get 20 ohms for the answer.


EDIT:
OK I tried this>>
Calculated first row>> 10+20+30 = 60
Then 1/60 = 0.01666 Then 3*0.01666 for the 3 rows = 0.04998
Then 1/0.04998 = 20.008
Which is just slightly over 20 ohms.
 
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john monks

Mar 9, 2012
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You have three identical strings of resistors. What is the total resistance in one string?
When you add resistances is series what happens to the total resistance?
What happens to the resistance when you combine resistances in parallel?
Does it increase or decrease and by how much?
An ohm is a unit of measure.
A volt is a unit of electromotive force.
An ampere is a unit of current.
These are your necessary definitions.
The current through a resistor is proportional to the voltage across it.
This comes from experimentation or the science.
If you don't know get two resistors and an ohmmeter and find out.
Now you have enough information to solve the problem.
If you are still stuck tell me what the total resistance of three 10 ohm resistors is parallel is and we will take it from there.
 

acidblue

Jul 11, 2012
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Total R in series is 30 ohms. R1+R2+R3
Total R in parallel is 3.33 ohms. >>1(1/R1)+(1/R2)+(1/R3)
 

john monks

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You are half correct. Lets look at this another way. If you have two 100 watt light bulbs plugged into the outlet the utility is now putting out 200 watts correct? so if one light bulb as X ohms of resistance, how much is the new resistance in terms of X? You see what I am trying to do is completely pull you away from the mathematics and to look only at the circuit just as if you never heard of ohms law. Another way to look at this is to hook up a battery to your circuit, calculate how much current is traveling in each branch, and then calculating what the total current is. If one branch draw X amps how much do the three branches draw in terms of X. Remember that your total conductance is directly proportional to your total current drawn and inversely proportional to your resistance. Please take another crack at this. You will discover that you are applying the wrong equation. There are many right equations and I am trying to get you to figure out one of them based only on science and definitions.
 

john monks

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That is wrong. Maybe I'm looking at the wrong thing. Are looking one branch or one string of resistors, a 10 ohm, 20 ohm, and a 30 ohm?
Maybe you should just assume a fixed voltage across all the string of resistors, calculate the current for each one, figure out the total current, the from that answer figure out the resistance of the whole circuit. Remember, your resistance is inversely proportional to your current.
 
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(*steve*)

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1(1/R1)+(1/R2)+(1/R3)
So wait this is wrong??

There's nothing wrong with that formula.

I think you've got the concept of series and parallel mixed up in your head.

Series is when you connect them up in a long chain, sort of like a group of people holding hands while waling along

Parallel is connecting them like the rungs of a ladder, or people in a line with their arms on the shoulders of the person in front of them.
 

Laplace

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So question #2 asks for the total resistance of the resistor network. Have a look at a similar example with different values. Due to the structure of the circuit, one must first combine the series resistors into an equivalent valued resistor. Then combine the parallel resistors into an equivalent valued resistor. It should be immediately obvious how the equivalent values are obtained.

Apply the same method to your problem.
 

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(*steve*)

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EDIT:
OK I tried this>>
Calculated first row>> 10+20+30 = 60
Then 1/60 = 0.01666 Then 3*0.01666 for the 3 rows = 0.04998
Then 1/0.04998 = 20.008
Which is just slightly over 20 ohms.

Near enough for government work. :)

Try it with more decimal places. Or more appropriately -- Step away from the calculator and do it using fractions.

Then see if you can find a relationship between the number of identical resistors in parallel, their individual resistance, and the final overall resistance.

Once you see that, you'll be able to look at the circuit and tell us the answer immediately without doing more than some trivial adding up in your head.
 
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