Hey guys. Simple question: what am I doing wrong?

Now I solve this and get a resistance of 1.6Ohms.

Ignore 2 & 3 as there is a short, so you get 4 & 4 in parallel. This is then in series with the next 4 to give a 6. The 6 is in parallel with the next 6 to give 3, which is then in series with the remaining 5 to give 8. This 8 is in parallel with the 2 giving a resistance of 1.6Ohms.

On the mark scheme it has the equation (8*2/8+2) to give the 1.6Ohms.

My question is, why didn't they just use the resistors in parallel equation and what does the potential/resistive divider equation actually do?

At the moment I don't see much point in it from that, so if you could explain why it is useful like that then that would be great. Thanks

 

The x/+ equation is so limited that I never use it. I guess some people think they are doing you a favor to teach you one form that is only useful for 2 resistors. I ran this circuit using exclusively N, invert, store, N, invert, sum, recall, invert before I read the question. You will probably end up doing this too, if you do it much. Your brain just won't bother to store equations that only have one use when you can use a "universal" form that works for any number of resistors.

 

So there is no real reason for it? It is just a 'shortcut' for if you only have two parallel resistors? So either way is fine?

Although seems rather pointless and just an extra thing to remember. Using 1/Total = 1/R1+1/R2 isn't exactly hard is it!

 

My question is, why didn't they just use the resistors in parallel equation and what does the potential/resistive divider equation actually do?

Your reasoning to arrive at 1.6Ω is correct.

It is a matter of personal taste whether you use 1/R = 1/R1 + 1/R2 or their formulae.

You should receive equal marks for either.

However if you have a special value to make up, there is an old formula, similar to theirs

If you want a special value Rd
Select a higher preferred valueR2

Then the shunt to make Rd is R2*Rd/(R2-Rd)

I do not understand the difficulty with potential dividers, perhaps you would tell us more?

 

My calculus teacher called it, "Maturity".
1/Rt = 1/R1+1/R2+1/R3... is an infinite series (if you need it to be infinite).
When you have the math maturity to think at that level, equations that only have one purpose become disused and almost forgotten.

After I had done college algebra, trig, and calculus, I got tripped up on a hypotenuse problem because I couldn't remember that far back!

A person that is only going to take, "Intro to Electricity" and never get above algebra might stop at the x/+ formula. If you're going to be a real engineer, you will pass that level of thinking so fast!

 

I would venture that we are dealing with a few different situations here.

The first is if someone is an equation monkey and only sees two equations without understanding either of them, let along recognizing that one is a special case of the other, and thinks that they are two different equations and that they have to be given a set of rules for when to use one and when to use the other. That's either someone that is very, very new or someone that has never (and probably will never) become anything other than an equation monkey. They are often typified by having to look up even most basic equations that they need because they are overwhelmed by how many of them there are.

The second is someone that has reached the point of understanding that they can minimize the number of equations they have to memorize by discarding the special case ones, allowing them to regurgitate the general case ones at need and apply them by rote.

The third stage is someone that has reached the point of understanding the underlying concepts well enough that they can derive many/most of the key general equations on the fly fast enough that they may as well be memorized. They tend to also just remember the more useful special case equations because they have internalized the concepts that link them to the general equations well enough. Hence, they can use whichever is more appropriate in a given situation.

For instance, in this case you can reduce it to 8Ω||2Ω by inspection. At that point, if all you remember is the general form, then you either have to go pick up your calculator, grab a pen and pencil, or be reasonably good at picturing the math in your head so that you can go something like:

1/8Ω + 1/2Ω, Okay, I need to get it over a common denominator, which is 8Ω, so I need to multiply the 1/2Ω by 4 (top/bottom) so that now I have 1/8Ω + 4/8Ω giving me 5/8Ω. Flipping that I have 8Ω/5. Multiplying top and bottom by 2 gives me 16Ω/10 which is 1.6Ω.

Doable, but takes longer and prone to making a goof along the way.

But if you've internalized the special case, then you just go something like: The product is (8Ω*2Ω), or 16Ω², and the sum is (8Ω*2Ω), or 10Ω, so the result is 1.6Ω. Done, with little chance for error.

Now, if you almost never see just two resistors in parallel, then the special case would not be worth internalizing. But, for most people, two resistors in parallel is the large majority of cases they will see, so it is worth internalizing.

On a related note, you could also argue that you don't need the reciprocal equation at all if you have memorized the two-resistor equation, since you can always reduce N resistors in parallel to a collection of two-resistors-in-parallel. And there are lots of people at the equation monkey level that do exactly that. They manage to memorize the two-resistor equation simply because they use it so much. If you give them three resistors, they will combined two using that formula and then combine that with the third. They will use that approach if you give them five resistors in parallel -- even if they are all the same value! Why? Because they haven't memorized the general equation (and that is all they are doing, memorizing equations). Even people that have memorized both, but don't understand the concepts, will use the general equation to find the value of N identical resistors in parallel.

I've seen it interviews. Gave them a circuit that, under the conditions of the question resulted in four equal 1kΩ resistors being in parallel. They started punching numbers furiously into their calculator. By watching them it was apparent they were plugging into the recipocal equation. I stopped them and asked what the resistance of four identical resistors of value R was and they gave me a blank look. I then said something like, "Well, if you have two resistors, the resistors, the current divides evenly and so you have half the current in each, and so half the voltage. So what if you have four resistors?" They looked at me blankly. I said, "Won't the current divide evenly?" They responded, "Oh. So half the current goes through each resistor." I figured it was just a mental blunder, so I said, "But there are four resistors, so you won't get half the current in each one." To which they said, "But you just told me that the current would divide evenly." To which I responded, "Oh, I see I've run us out of time. It was nice talking to you."