# Total Resistence in Parallel circuit

#### AWSariti

Joined Nov 27, 2004
7
For newcomeres like me, a thought on this.

Sometimes texts tell us "that" something is so-and-so, but not "why." For example, total resistence in a series circuit is the sum of the resistences. Or, total resistence of a parallel circuit is less than the smallest resistence. This tells us "that" but not "why."

The series circuit is intuitively easy to understand. You have resistences, one after the other, they add up -- makes immediate sense. You don't have to really get into the "why" on this one.

But the parallel circuit is different, at least to me and some others I've talked with. Somehow, it's not immediately apparent that the "total" resistence is less than the lowest resistence, i.e., the lowest resistor in the circuit. Obviously, using the "water pipe" analogy gives an immediate, intuitive understanding that the total resistence of a parallel circuit is less than the sum of the resistences/resistors. But that the total resistence is less than the smallest resistor -- that comes as a surprise. The question is "why" is this true. How do you conceptualize this for the student? Here's my take.

Let's take a circuit with three resistors, 10, 20, 30 ohms. When the current moves into the circuit it splits up and proceeds to move across each resistor at a certain speed depending on the amount of resistence encountered, the pressure (voltage) being the same for all. They move across the lowest resistor at the fastest rate among the three resistors. The elctrons move across the 20 and 30 ohm resistors at a slower rate, but some do go across.

Now to conceptualize it, a certain number of electrons go across the 10-ohm resistor in a certain amount of time. With a predetermined amount of pressure (voltage) and the resistence/resistor remaining the same, the number of electrons going across the resistor is set and cannot in these circumstances change. Thus if the circuit only had this one resistor, the number of electrons getting to the other side would be the same. In other words, the rest of the circuit is irrelevant if we just focus on this one "electron bridge." Now, in the parallel circuit, while these electrons are moving their merry way across the 10-ohm resistor at a speed/amount determined by the pressure (voltage) and the resistence in the resistor, other electrons are not just waiting in line, they are going over the other two resistors, albeit at a slower pace.

Thus, in a certain period of time, the electrons moving across the 10-onm resistor are joined on the other side by electrons that have gone through the 20 and 30-ohm resistor "bridges", even if they have gone over at a slower rate because the resistence was higher. So, overall, there are more electrons that make it over the various bridges in a certain amount of time than get over just the one "bridge" of the 10-ohm resistor. So, overall, there is lower resistence in the circuit, because more electrons get to the other side of the circuit that those just going across the 10-ohm resistor/bridge.

Long-winded, but this "why" the overal resistence of resistors in parallel is less than the resistence of the lowest resistor.

Joined Jan 19, 2004
220
yup thats precisely why the resistance of a parallel combination is lower then the lowest resistance and it permits more current thru it than the lowest resistance connected thru it

#### beenthere

Joined Apr 20, 2004
15,819
Hi,

You might tie your head in fewer knots if you just consider that each resistor in a parallel circuit has the same voltage across it. That means that the total current in the circuit will be greater than if only the lowest value resistor were in circuit alone. And it then follows that the total resistance must be less than that of the lowest value resistor for that to be true.

#### Martin P Dembrowski

Joined Dec 3, 2004
10
HI Guys...

These are the areas of electronics that I know best, the very basic ones. I've always been a very intuitive type and I've always spent inordinate amounts of time trying to conceptualize and express what it is I think I know. I've put the "flow and resistance" thing into more different ways then I think practical, maybe. But if you think of the sheer fact that the more room you give for the traffic, on a road or highway, in pipes, hallways at school, getting through a doorway, the bigger the opening the easier it is to pass more and more through at the same time. More hallways or roads connecting the same points are just as good as a wider, less resistive one.

The concept of "less then the least resistance" should be intuitive if thought of from the reciprical view of conductance, you have the "conductance" of the one and now an additional path that lets a total of "more" pass by another route. How many more people could migrate in and out of New York City at rush hour if they doubled the amount of bridges and tunnels into Manhattan? Okay, tripled? Triple the amount of cars, trucks and busses would be able to go (considering a linear extrapolation of the formula not accounting for unforseen problems elsewhere in the picture) which is, of course, more then the greatest bridge or tunnel existing could handle on it's own, right? The widest bridge or tunnel should carry the most traffic and so is the least resistive, or the highest conductance. More bridges and tunnels, more traffic, highter conductance, lower resistance than the lowest "single" bridge in the plan, right?

In this case, think "conductance" and think about how many more electrons are given the chance to race accross to the finish line "at the same time".

One thing I want to point out. The electrons won't travel any slower or faster, just the volume increases or decreases on change of resistace or conductance. This may help the conceptualization a little.

Thanx for letting me butt-in! Joined Jan 19, 2004
220
i d recommed u butt in more often.... its a rare for an indian student to view the concept at the root level.. primarily bcoz no-one here gives a damn to concept...its only the marks that count here..
change in the rate of flow of chrge implies 2 things
1. either the no of elcetrons flowing changes or
2. the spped of electron flow changes.
u sya the latter doenst occur
why??

#### Martin P Dembrowski

Joined Dec 3, 2004
10

I'm sorry it took me a while to get back to you but you will appreciate all the work one has to do if you are in school/college. I'm not in school but I still have other work. I have some links and I think I know where your concerns are originating. After knowing this basic area of electronics for some 40 years now I've come to understand that the simple fact that since velocity is not a component of Ohm's Law it must be irrelevant (not needed to know the velocity of an electron to solve the voltage, resistance, current equation), which is the case here:

E=IR or V=IxR

Since a velocity component isn't a part of Ohm's Law and we don't have to worry about it's value we can consider the electrons to always flow at the same velocity. I grant you that, yes, under different circumstances they have different energies and velocities, but again since we are talking about a situation in which all the current can be assumed to be in the same or similar material under the same ambient conditions they are essentially identical in all of their properties including typical velocity.

A statement that I found on the third link listed below reads:

Metals are good conductors because they have unfilled space in the valence energy band. In the absence of an electric field, there exist electrons travelling in all directions and many different velocities up to the Fermi velocity (the velocity of electrons at the Fermi energy). When an electric field is applied, a slight imbalance develops and a current flows. Electrons in this band can be accelerated by the field because there are plenty of nearby states on the band.

Herein lies the reason for my statement. The discussion implies that they are a randomly moving body in the absence of an electric field, the condition which is necessary to cause our situation in the first place. The implication here is that the movement of electrons is orderly (+/-) in the presence of an elecrtic field. I would consider that to include velocity.

This is only as I see it. I'm not a PhD or engineer, I'm an amateur radio operator, but we have to learn quite a bit of electronics to get our "tickets". If you are dissatisfied with this conclusion I encourage you to ask about. It won't insult me, I understand getting as many viewpoints as you can handle. Here are some pages that might help you understand my point:

http://www.sengpielaudio.com/calculator-ohmslaw.htm
http://en.wikipedia.org/wiki/Ohm%27s_Law
http://en.wikipedia.org/wiki/Conduction_electron

But my advice is not to complicate a situation and leave out worrying about things that don't even enter the equation, okay?

Good luck and nice to meet you!
Martin

#### Schmooster

Joined Dec 7, 2004
1 all these explanations merely serve to confuse imo, fine if you're explaining it to someone who understands (and I do) but I doubt very many students would come away from this post thinking 'ah, so that's why' No offense to anyone intended, you're very intelligent and it shows, but what about a very basic grasp of this? As someone has said, there's no need to unecessarily complicate things, and once understood, always understood. I'm sure I wouldn't remember anything I've read here this time tomorrow.
Here's my attempt:

Imagine a circuit with a 10 ohm resistor, you know current is flowing and it doesn't matter how much just yet. Let's add another 10 ohm resistor in parallel. Ohms law tells us we now have twice the amount of current flowing in the circuit. If there's twice the current then it follows that it must be half as resistive than it was with just the 10 ohm resistor, which would be 5 ohms resistance, and we all know it is, and now we all know why. Yep, I can confuse me just as good as you can! Nice board btw.

• irulu.electrical

#### electro eto

Joined Oct 5, 2006
4
i personally believe that all this wordind are irrrelevant. because lookin at the formular for find the current flow in a parallel circuit and compare to a series circuit anyone should grasp the reason and how ohm came to a conclusion about how the currend are distrbuted across every resisitor. ohms law explained it all. jus look over the formular once more. you should understand from there. all this word stuff on complicate the whole thing.

#### Nirvana

Joined Jan 18, 2005
58
Hi there here is the proof of the parallel resistor network. I can do another one if you would like the Rtotal = R1R2R3/R1 + R2 + R3, the attachment shows the proof of 1/Rtotal = 1/R1 + 1/R2 + ... 1/Rn

Hope this helps
Nirvana.

#### Salgat

Joined Dec 23, 2006
221
The path of least resistance is the path through which most current travels, which is why a short circuit results in the total resistance of that short circuit and all resistors in parallel with it being almost 0. A simple concept it would seem... Same thing as if you had 3 pipes through which water has to travel through. The pressure is equal upon all 3 pipes but the one of least resistance will take in the majority of water, leaving only a little water to flow through the other 2 pipes, resulting in low resistance overall.

#### Avalanche Breakdown

Joined Mar 22, 2007
20
New here, and first post. Hardly know a darn thing about electricity, or circuits, as I will prove with a couple questions later tonight (after getting back from work).

OK, I already knew the answer regarding parallel resistance. However, it's surprising to hear that electrons can move at different speeds! My assumption was that electron velocity is always the same in any material, and that variables like conductor temperature, choice of conductor, etc., only affects volume of flow (resistance). In other words, I thought electrons were analagous to photons in that they only travel at one speed.

Is my assumption incorrect?

#### recca02

Joined Apr 2, 2007
1,214
well under the application of a potential difference the the electrons must acually accelerate but due to constant collisons the speed gets down to a constant drift velocity. the speed hence i believe is variable under application of higher voltage.

#### thingmaker3

Joined May 16, 2005
5,084
Photons also travel at different speeds in different media. This is why prisms and lenses work. #### Avalanche Breakdown

Joined Mar 22, 2007
20
Photons also travel at different speeds in different media. This is why prisms and lenses work. Heh... probably been told that before (like in high school science), and forgot.

So, refraction is a function of speed? By virtue, does that explain why a prism splits light into it's constituent colors?... meaning, different wavelengths travel through the same media at different speeds?

Also, is it the 'changing' of photon speed that produces the bending of light in a lens or prism?

[/hijack]

#### royalt213

Joined Feb 27, 2009
3
Nirvana,

Thank you very much for that proof. I haven't even looked at it yet, but this is what I was looking for. It's amazing how hard it can be to find proofs and/or explanations on the internet sometimes!

Taylor

Hi there here is the proof of the parallel resistor network. I can do another one if you would like the Rtotal = R1R2R3/R1 + R2 + R3, the attachment shows the proof of 1/Rtotal = 1/R1 + 1/R2 + ... 1/Rn

Hope this helps
Nirvana.