Resistor and current in a circuit

[conscience]

Hello ,

I have to teach a group of 9th grade students
role of resistor in a circuit and how it affects the current in the circuit . This will be their first exposition to circuits .So I need a good and simple analogy so that students can grasp these concepts easily .

This is what I plan to teach .

Consider two set ups . In first there is an inclined plane with lots of balls held at the top .Now these balls are allowed to roll down the plane one after another .The number of balls collected per unit time at the bottom is noted , say x balls/sec .

In the second case , there are pegs/ obstructions on the inclined plane such that if a ball is released at the top ,it will reach at the bottom only after bouncing off from the pegs in a zig zag fashion .Again the number of balls collected at the bottom is noted ,say y balls/ sec .

Clearly x>y .

The first case represents a very low resistance wire connected across a battery and the second represents a high resistance connected across a battery .

The height represents potential difference .Balls are electrons , pegs are ions .

A child putting the balls back on top acts like a battery .

It can be seen that similar to the ball example , the current flowing in a circuit with a bigger resistance is lower i.e the resistor reduces the current in a circuit . Bigger the resistance offered , smaller the current .

Is this a decent analogy ? Is there something I am missing or something I need to correct .

Please give your feedback .

Thanks

 

[rumborak]

I think it's an excellent visualization. Usually people go for the "water flowing through narrowing pipes" analogy, but yours is closer to physical reality.

 

[conscience]

Great !

Another question that one of the more curious minds can put is -

" Why/How is current constant in a circuit " ?

This is what I think -

1) Because of law of conservation of charge , charge flowing in per second in any part of the circuit is equal to charge flowing out per second . Current has to be same .

2) Even if we suppose that current is not uniform , then there would be a build up of charge somewhere .This would ensure that faster moving electrons are slowed down whereas slower moving electrons pick up speed .

Alternatively, mutual repulsion of electrons will ensure that electrons are moving with a constant average speed .

Is this a valid explanation ?

 

[cnh1995]

Great !

Another question that one of the more curious minds can put is -

" Why/How is current constant in a circuit " ?

This is what I think -

1) Because of law of conservation of charge , charge flowing in per second in any part of the circuit is equal to charge flowing out per second . Current has to be same .

2) Even if we suppose that current is not uniform , then there would be a build up of charge somewhere .This would ensure that faster moving electrons are slowed down whereas slower moving electrons pick up speed .

Alternatively, mutual repulsion of electrons will ensure that electrons are moving with a constant average speed .

Is this a valid explanation ?

Yes.

And for point no 2, mention that the time of the surface charge build-up is in the order of
10^-10 to 10^-12 s, which is why we see a lightbulb glowing instantly after the switch is closed.

 

[davenn]

2) Even if we suppose that current is not uniform , then there would be a build up of charge somewhere .This would ensure that faster moving electrons are slowed down whereas slower moving electrons pick up speed .

no, this isn't a good way to look at it

electron drift is very slow a few mm per second
the current in a circuit is the number of electrons ( charges) passing a particular point in a circuit at a given time, not how fast they are travelling

 

[davenn]

Yes.

do you want to clarify your simple yes ?
it can't be used as a blanket response for both his comments

 

[cnh1995]

do you want to clarify your simple yes ?

Because of law of conservation of charge , charge flowing in per second in any part of the circuit is equal to charge flowing out per second . Current has to be same .

This is correct.

But initially, when the circuit is closed (say using a switch), this is not true. To make the current same everywhere in the circuit, there are surface charge buildups on the wires and circuit components.

I agree that speed of electrons is not the correct way to visualize current.
Instead, in point no 2, he should say: The surface charges build up because initially, the charges move at different rates, which results in excess positive charge in some parts and excess negative charge in some parts. This process goes on until there is no excess charge in any part of the circuit i.e. charge is flowing at the same rate everywhere.

 

[cnh1995]

of why current in a circuit is constant ?

Do you mean to ask "why current in a series circuit is same everywhere?".
The word 'constant' has different interpretations.

 

[conscience]

Yes.

I am not comparing two different circuits . I just want to explain to somebody why a simple circuit consisting of a battery and a resistor has constant/same current throughout the circuit .

If somebody says , why can't current be different in different parts of a circuit ? What would be an explanation at an elementary level ?

Point 2) to which davenn had objected was an explanation for a hypothetical assumption .

Why number of electrons crossing an area per unit time has to be equal to that in some other part of the circuit ?

 

[cnh1995]

Why number of electrons crossing an area per unit time has to be equal to that in some other part of the circuit ?

The surface charges build up because initially, the charges move at different rates, which results in excess positive charge in some parts and excess negative charge in some parts. This process goes on until there is no excess charge in any part of the circuit i.e. charge is flowing at the same rate everywhere.

 

[conscience]

I might be wrong but I think this is an explanation to how uniform electric field is establiahed within the circuit .

Anyways my audience is 9th graders learning circuits for first time .I think it would be difficult for them to understand .

 

[Tom.G]

Why number of electrons crossing an area per unit time has to be equal to that in some other part of the circuit ?

If there are sidewalls on the inclined plane to eliminate spillage, point out that there are the same number of balls flowing at the bottom as at the top because there is no other place for them to go.

 

[conscience]

no, this isn't a good way to look at it

electron drift is very slow a few mm per second
the current in a circuit is the number of electrons ( charges) passing a particular point in a circuit at a given time, not how fast they are travelling

How about this explanation -

The electrons are moving with approximately uniform average speed .So if I consider a piece of wire and assume that current at its two ends are different than this means that some charge carriers are appearing/disappearing magically .This can't happen .

Is it alright ??

 

[conscience]

If there are sidewalls on the inclined plane to eliminate spillage, point out that there are the same number of balls flowing at the bottom as at the top because there is no other place for them to go.

Ok.

Actually what is troubling me is not the number of balls starting at the top and ending at bottom , but the rate of flow of balls .

I think speed is an important factor .

Do you think students also need to be told beforehand that average speeds of all the electrons in the circuit is same just like same average speeds of all balls on the inclined plane ??

 

[cnh1995]

I might be wrong but I think this is an explanation to how uniform electric field is establiahed within the circuit .

The field is not necessarily uniform.
The surface charge buildup stops only when there is no excess charge in any part of the circuit i.e. rate of flow of charge is same everywhere.

This phenomenon gives you the idea/ explanation to some FAQs from high school students like, as you said, why current is same everywhere?, why doesn't current drop after passing through a resistor?, how do electrons turn on a bend in the circuit or why does the shape of the circuit not matter in circuit analysis? etc.

But since it is their first-time with circuits, this might be difficult for them to understand (they may not be knowing anything about electric field or relevant electrostatics).
So I think you should drop this approach.

 

[Tom.G]

Ok.

Actually what is troubling me is not the number of balls starting at the top and ending at bottom , but the rate of flow of balls .

I think speed is an important factor .

Do you think students also need to be told beforehand that average speeds of all the electrons in the circuit is same just like same average speeds of all balls on the inclined plane ??

I agree that "...the rate of flow of balls" is the key factor.

Since Electron speed is constant in a given medium, I would be careful about how this is presented. I'm afraid your ramp with pegs will have an observably longer transit time than the ramp without pegs. Even though the "electrons bouncing off atoms" explanation is widely used, and understandable, it is an analogy and therefore imperfect.

I originally visualized the demo hardware as a reservoir at the top emptying to an unpopulated ramp. Perhaps you had something else in mind?

If the ramps (w/ & w/o pegs) are initially filled with balls, as a wire is filled with Electrons, the (almost) instantaneous flow at the bottom would more correctly show the immediate current flow in the real world. This would probably require that the demo starts with the ramp horizontal. Then raising the reservoir end to show a battery being connected. Practically, this may require a gate at the ramp bottom and a bit of hand-waving that you can't really raise the reservoir as fast as a switch closes.

edit: p.s. "The electrons are moving with approximately uniform average speed"
This polysyllabic exposition may be a stretch for the vocabularies of some 9th graders.

 

[conscience]

@cnh1995 , @Tom.G

What are your thoughts on post 13 ?

 

[Tom.G]

What are your thoughts on post 13 ?

See my edit to post #16.

 

[conscience]

See my edit to post #16.

OK . But do you find it reasonable ?

 

[davenn]

@cnh1995 , @Tom.G

What are your thoughts on post 13 ?

How about this explanation -

The electrons are moving with approximately uniform average speed .So if I consider a piece of wire and assume that current at its two ends are different than this means that some charge carriers are appearing/disappearing magically .This can't happen .

Is it alright ??

no

I gave you the answer and you quoted it in post #13
why give another incorrect reason in that post ?

 

[conscience]

no

I gave you the answer and you quoted it in post #13
why give another incorrect reason in that post ?

I understand that current is charge flowing past a point per second . But it is the rate of flow and not simply the amount of charge flowing .

So if I start with the assumption that current is different at two different points , how will we refute this assumption while not taking electrons drift speed into account .

Please explain your objection to post 13 .

 

[Tom.G]

The electrons are moving with approximately uniform average speed .

What are your thoughts on post 13 ?

conscience said: ↑
How about this explanation -

The electrons are moving with approximately uniform average speed .So if I consider a piece of wire and assume that current at its two ends are different than this means that some charge carriers are appearing/disappearing magically .This can't happen .

(from: davenn post #20)
Is it alright ??
no

I gave you the answer and you quoted it in post #13
why give another incorrect reason in that post ?
(/davenn)

I think I'm getting into the middle of a dispute here! Ahh, well. Not the first time. (sigh...)

I don't see any conflict between
@conscience in post #13 as "...moving with approximately uniform average speed" and moving at a specific speed that @davenn reported in post #5 as"... a few mm per second."
Perhaps the perceived conflict is from the impracticality of having a ramp for the demo wide enough to accommodate all the electrons in a wire. With this constraint, the balls in the demo will be moving faster than real electrons. This may well be necessary to avoid having the class fall asleep during the demo!

But it is the rate of flow and not simply the amount of charge flowing .

There are at least two interpretations of rate. Specifically, "The rate that a river flows in miles-per-hour" and "the rate the river flows in gallons-per-second."

In Physics, current is defined in terms of Electrons-per-Second, and the miles-per-hour or mm-per-Second is irrelevant to current measurement.

It sounds like different folks are reading the same word and using different definitions.

 

[cnh1995]

So if I start with the assumption that current is different at two different points , how will we refute this assumption while not taking account electrons drift speed .

Drift speed alone is not the correct way to visualize current. You can have 100 electrons drifting with 1mm/s and 50 electrons drifting with 2 mm/s, but both of them give the same current. In a series circuit, the drift speed is different in different components but the current through them is still the same.

 

[conscience]

Drift speed alone is not the correct way to visualize current. You can have 100 electrons drifting with 1mm/s and 50 electrons drifting with 2 mm/s, but both of them give the same current. In a series circuit, the drift speed is different in different components but the current through them is still the same.

I agree .

Do you have a simple explanation as to why should current be the same ?

 

[davenn]

I agree .

Do you have a simple explanation as to why should current be the same ?

cuz what goes into the circuit MUST be the same as what comes out of the circuit. Regardless of what happens within the circuit
If it is a simple series circuit, the current will be measured the same everywhere in the circuit
in a complex circuit, current will be different in different parts BUT overall what goes in is the same as what comes out

imagine a black box ( you DONT know what is inside the box) with 2 wires and an ammeter in each wire.
when you connect it to a power source, the current in each meter will read the same REGARDLESS of what circuitry is inside the black box

 

[davenn]

Drift speed alone is not the correct way to visualize current. You can have 100 electrons drifting with 1mm/s and 50 electrons drifting with 2 mm/s, but both of them give the same current. In a series circuit, the drift speed is different in different components but the current through them is still the same.

and isn't even used in the calculations

I understand that current is charge flowing past a point per second . But it is the rate of flow and not simply the amount of charge flowing .

So if I start with the assumption that current is different at two different points , how will we refute this assumption while not taking electrons drift speed into account .

Please explain your objection to post 13 .

because you don't need to take drift speed into account, you have been told this.
drift speed varies very little unless you are dealing with comparing very small and very large currents

the important information is the quantity of charges flowing NOT their speed

from wiki

The SI unit for measuring an electric current is the ampere, which is the flow of electric charge across a surface at the rate of one coulomb per second. Electric current is measured using a device called an ammeter.[2]

The coulomb (symbol: C) is the International System of Units (SI) unit of electric charge. It is the charge (symbol: Q or q) transported by a constant current of one ampere in one second:
1 C = 1 A ⋅ 1 s Dave

 

[conscience]

cuz what goes into the circuit MUST be the same as what comes out of the circuit.

But why should what goes into per second should be what goes out per second in any arbitrary section of circuit ?

Please consider any portion of the circuit and not specifically from one terminal of battery to other .

 

[davenn]

But why should what goes into per second should be what goes out per second in any arbitrary section of circuit ?

physics doesn't answer why questions ... it's the way it is

https://www.farnamstreetblog.com/2012/01/richard-feynman-on-why-questions/

you put x litres of water into one end of a pipe, x litres will come out the other end ( assuming the pipe is already full)

the same with a bit of wire or a circuit ... it is already at equilibrium
when 500 electrons leave the negative terminal of a battery ( or other power supply) and enter the circuit, it will create an imbalance in the circuit and in the battery (PSU) and via the force from the electric field
those 500 electrons will be moved slowly along the wire/circuit and will get back to the power source to restore equilibrium

 

[Dale]

Anyways my audience is 9th graders learning circuits for first time .I think it would be difficult for them to understand

Why do we need to do complicated analogies with balls bouncing down pegs at all? Why not just teach V=IR?

It is so simple that I don't think it needs an analogy. Even 9th graders can do it. Any analogy is going to be more complicated and less accurate than the real thing.

 

[Dale]

So if I start with the assumption that current is different at two different points , how will we refute this assumption while not taking electrons drift speed into account .

One of the assumptions of circuit theory is that the net charge on any component is 0 at all times. If the current in and out of any component were unequal then that component would have a nonzero net charge.