How Do You Calculate Resistance in Complex Parallel and Series Circuits?

[JEV]

Homework Statement

Calculate the resistance across AO and BO

----------------------|-----------------|
|...... | ..... |
|..... --- ..... ---
|...... | x |... | x |
|...... | x |... | x |
V..... --- ... ---
|...... | A.....| B
|.....|......|
|......---......---
| ..... | x |... | x |
|...... | x |....| x |
| ...... ---...... ---
|...... | ..... |
-------------------------------------------
|
O

Homework Equations

V=IR
R=R1+R2 in series
R=1/((1/R1)+(1/R2))

All Resistors are 100 ohms

The Attempt at a Solution

I know that if one of the branches wern't there that it is a simple case of a parallel circuit and so the resistance is 1/R = 1/100 +1/100 = 1/50 therefore R across AO would e 50 ohms however I don't know what to do when the second branch is to be included.

Also sorry about the diagram i wasn't sure how to draw it the spaces just dissapeared, the . indicate free space and the x's show the positions of the resistors

 

[Zryn]

Is this how the picture is meant to be?

 

[JEV]

Yes thank you.

 

[Zryn]

I know that if one of the branches wern't there that it is a simple case of a parallel circuit and so the resistance is 1/R = 1/100 +1/100 = 1/50 therefore R across AO would e 50 ohms however I don't know what to do when the second branch is to be included.

If the right most branch disappeared (as in the new picture) and you were left with the following, what would the type of circuit be (serial or parallel?), what would the total resistance be, and what would the resistance between A and O be?

 

[JEV]

If the right most branch disappeared (as in the new picture) and you were left with the following, what would the type of circuit be (serial or parallel?), what would the total resistance be, and what would the resistance between A and O be?

I was taught that if it was as in the new image then across AO the circuit can be considered parallel so you use 1/R

 

[JEV]

How we were taught.

 

[Zryn]

In your picture, if you look at where the two resistances are connected, they are both connected at the same point, whereas in the other diagram they are connected at different points.

This is a good way to look at whether resistances are in series or parallel. Draw the picture, and highlight all the wires each point is connected to.

 

[JEV]

I understand that if i were looking for a total resistance i would just add the resistors, but as I am looking for this resistance across point A and the ground then it is different.

 

[Zryn]

I think I'm misunderstanding something somewhere sorry.

Are you asking what the resistance is of the single element between points A and O, when you are told initially that each resistor is 100 Ohms?

 

[JEV]

The Question is,

Calculate the resistance across AO

Calculate the resistance across BO

 

[Zryn]

Do you have answers to this question?

 

[JEV]

Well I have answers to a similar set up where the resistors were 120 ohms and the resistances were 60 for both AO and BO but i need to know how to get these values.

 

[Zryn]

Edit: Delete misinformation.

 

[JEV]

This is the problem i have been having, i just don't see a logical way to get the answers i am given, i shall try and meet with the lecturer and see if hecan shd some light on it, cheers for trying anyway.

 

[Zryn]

If you consider Ohms law, for example assign a voltage of 10V (or do it algebraically), then find the current split between each (equal) branch, and then use the current with the voltage division, what answer do you get for each resistance?

 

[Zryn]

Does this picture help?

*I've led you astray by saying there was only 1 resistance, you still have to take into account the other resistances, which is why it seemed too easy and why I was misunderstanding the point of the question. My apologies .

 

[vk6kro]

Since V is not given and it is irrelevant, assume it is zero and replace it with a short circuit:

[PLAIN]http://dl.dropbox.com/u/4222062/R%20prob..PNG

Now it is a simple problem with two sets of parallel resistors in series.