# Challenging resistance calculation

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#1
I found this question posted by StoneBridge some where. Anyway, I didn't really quite get it because I just confused things up and that's due to my lack of understanding to certain topics.

How i thought about it is using the idea of short circuit which is totally wrong, but i want to know why it won't work here? and if can be explained by it, how?
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6 years ago
#2
It looks like only the middle resistor wouldn't work while the other two are in fact parallel with each other?
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6 years ago
#3
(Original post by Daniel Atieh)
I found this question posted by StoneBridge some where. Anyway, I didn't really quite get it because I just confused things up and that's due to my lack of understanding to certain topics.

How i thought about it is using the idea of short circuit which is totally wrong, but i want to know why it won't work here? and if can be explained by it, how?
Think of the problem as one of voltages and currents. Using one terminal as a reference, what would the potential differences (voltage drops) around the circuit look like? Where would the current flow in a dc circuit first and then consider the same question for an ac circuit.

HINT:

Spoiler:
Show

Try redrawing the circuit with a dc power source on the lhs between A and B and the three resistors arranged on the other three sides of a square. Finally draw in the conductors and follow the current paths around the formed loops according to Kirchoff's rules.

The s/c's definitely need to be taken into account and you can work out the resistance by inspection alone for both ac and dc.
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#4
(Original post by uberteknik)
Think of the problem as one of voltages and currents. Using one terminal as a reference, what would the potential differences (voltage drops) around the circuit look like? Where would the current flow in a dc circuit first and then consider the same question for an ac circuit.

HINT:

Spoiler:
Show

Try redrawing the circuit with a dc power source on the lhs between A and B and the three resistors arranged on the other three sides of a square. Finally draw in the conductors and follow the current paths around the formed loops according to Kirchoff's rules.

The s/c's definitely need to be taken into account and you can work out the resistance by inspection alone for both ac and dc.
First of all, many thanks for your help, man! I'm pretty weak in this topic and I didn't quite follow all your points :/

When i first saw this question, i just followed the path of the current and imagined it in this way (which looks silly and incorrect):

So according to this diagram i drew, each resistor will receive a different current and therefore they re in parallel (i.e total R is R/3). I indicated each current by a different colour. So is my approach at least close to the correct way?

I m sorry, but as i said, am weak in this topic and your help here might contribute to a massive improvement in my understanding in such problems.

Thanks a ton once again!
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#5
(Original post by RoyalBlue7)
It looks like only the middle resistor wouldn't work while the other two are in fact parallel with each other?
I also thought like that in the first place, but the answer is R/3. I still didn't quite get how to approach to this answer exactly :/
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6 years ago
#6
(Original post by Daniel Atieh)
First of all, many thanks for your help, man! I'm pretty weak in this topic and I didn't quite follow all your points :/

When i first saw this question, i just followed the path of the current and imagined it in this way (which looks silly and incorrect):

So according to this diagram i drew, each resistor will receive a different current and therefore they re in parallel (i.e total R is R/3). I indicated each current by a different colour. So is my approach at least close to the correct way?

I m sorry, but as i said, am weak in this topic and your help here might contribute to a massive improvement in my understanding in such problems.

Thanks a ton once again!
It's sort of nearly there and gets the correct answer, you got the current loops going in the correct directions at least (though it actually doesn't usually matter).

Essentially all linear circuit problems come down to kirchoff's laws and the laws governing the components:

1. The sum of currents flowing into a node is zero. (Alternatively current into any point in a circuit is equal to the total current going out of it)
2. The voltage drop around ANY CLOSED loop is zero.
1
6 years ago
#7
(Original post by Daniel Atieh)
I also thought like that in the first place, but the answer is R/3. I still didn't quite get how to approach to this answer exactly :/
Let the voltage at A be V volts and that at B be 0 volts. The note that:

a) the 2nd node from the left is connected to B by a path of no resistance, so what is its potential?

b) the same question for the 3rd node from the left.

So

1. in which direction does the current flow through the central resistor and what is its magnitude?

2. the same question for the left and right hand resistors

That should give you enough info.
1
#8
(Original post by natninja)
It's sort of nearly there and gets the correct answer, you got the current loops going in the correct directions at least (though it actually doesn't usually matter).

Essentially all linear circuit problems come down to kirchoff's laws and the laws governing the components:

1. The sum of currents flowing into a node is zero. (Alternatively current into any point in a circuit is equal to the total current going out of it)
2. The voltage drop around ANY CLOSED loop is zero.
(Original post by atsruser)
Let the voltage at A be V volts and that at B be 0 volts. The note that:

a) the 2nd node from the left is connected to B by a path of no resistance, so what is its potential?

b) the same question for the 3rd node from the left.

So

1. in which direction does the current flow through the central resistor and what is its magnitude?

2. the same question for the left and right hand resistors

That should give you enough info.
Thanks a lot guys for your help So...

As the voltage drop in each loop is zero, so each of the resistors receives full voltage say V and therefore they re therefore in a parallel connection right?
0
6 years ago
#9
(Original post by Daniel Atieh)
Thanks a lot guys for your help So...

As the voltage drop in each loop is zero, so each of the resistors receives full voltage say V and therefore they re therefore in a parallel connection right?
Essentially you can write an equation for every closed loop in the circuit and then when you have enough you can solve them simultaneously.
0
6 years ago
#10
(Original post by Daniel Atieh)
I also thought like that in the first place, but the answer is R/3. I still didn't quite get how to approach to this answer exactly :/
Lol I forgot about Kirchhoof's (?) laws. Didn't realize that the current could flow the other way through the middle resistor. 0
6 years ago
#11
(Original post by Daniel Atieh)
Thanks a lot guys for your help So...

As the voltage drop in each loop is zero, so each of the resistors receives full voltage say V and therefore they re therefore in a parallel connection right?
Yes, this is simply a parallel arrangement of 3 resistors redrawn to disguise that fact.
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6 years ago
#12
Yes, I did post this question some years ago.
Here's the original post and the replies.
http://www.thestudentroom.co.uk/show...php?p=31142023
Yes, they are just 3 resistors in parallel.
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#13
(Original post by atsruser)
Yes, this is simply a parallel arrangement of 3 resistors redrawn to disguise that fact.
Yes, man. Can you show me how to write the equations and then solve them simultaneously using the example i posted above?

Posted from TSR Mobile
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#14
(Original post by Stonebridge)
Yes, I did post this question some years ago.
Here's the original post and the replies.
http://www.thestudentroom.co.uk/show...php?p=31142023
Yes, they are just 3 resistors in parallel.
Thank you!
Can you show me how i can develop two equations and then solve them simultaneously pls.
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