## Action potentials

Andy Maldonado, on Quora, writes

### An action potential is the way by which neurons communicate.

### Neurons are negatively charged on the inside and positively charged on the outside.

### This is due to the different concentrations of Na+, K+, Cl-, Ca2+, and charged proteins distributed both in and outside the neuron.

### An action potential begins when a disruption of this distribution causes Na+ to flow into the neuron, through Na+ channels, causing the inside to become more positive.

### The more positively charged inside of the neuron triggers adjacent voltage-gated Na+ channels to open and allow more ions to flow through.

### The increase in charge inside the neuron triggers K+ channels to open – allowing for ions to flow outside of the cell, and thus lowering the inside charge back to its original state.

### This increase and decrease in charge causes a wave-like motion of ions that propagates down the axon of a neuron – and ultimately causes the release of neurotransmitters from the dendrites – which stimulate the next neuron to either initiate or inhibit an action potential.

### Action potentials trigger neuronal pathways which can stimulate or inhibit certain functions in our body. For example, action potentials in the motor region of the brain may stimulate a neural pathway with leads to the muscles in your arms resulting in flexion. Action potentials also facilitate communication between neuronal networks in the brain which allow us to have conscious thoughts, emotions, and memories.

Animation

### As a nerve impulse travels down the axon, there is a change in polarity across the membrane.

The Na+ and K+ gated ion channels open and close in response to a signal from another neuron. At the beginning of action potential, the Na+ gates open and Na+ moves into the axon. This is depolarization. Repolarization occurs when the K+ gates open and K+ moves outside the axon. This creates a change in polarity between the outside of the cell and the inside. The impulse continuously travels down the axon in one direction only, through the axon terminal and to other neurons.

### External links

### http://blog.eyewire.org/the-nervous-system-action-potential-crash-course-2/

## Learning Standards

2016 Massachusetts Science and Technology/Engineering Curriculum Framework

HS-LS1-2. Develop and use a model to illustrate the key functions of animal body systems: Emphasis is on the primary function of the following body systems… nervous (neurons, brain, spinal cord).

College Board Science Standards

LSH-PE.5.5.4 Construct a simple representation of a feedback mechanism that maintains the internal conditions of a living system within certain limits as the external conditions change.

LSH-PE.5.5.5 Construct a representation of the interaction of the endocrine and nervous systems (e.g., hormones and electrochemical impulses) as they interact with other body systems to respond to a change in the environment (e.g., touching a hot stove). Explain how the representation is like and unlike the phenomenon it is representing.

## Ampère’s circuital law

I’m caching a copy of www.maxwells-equations.com/ampere/amperes-law.php

This isn’t to negate the copyright of the original website, which I direct people to! I create backups like this on occasion, because even favorite teaching websites sometimes disappear (maybe the owner didn’t pay to renew the domain name.) And I wouldn’t want something so valuable to disappear.

___________________

On this page, we’ll explain the meaning of the last of Maxwell’s Equations, **Ampere’s Law**, which is given in Equation [1]:

Ampere was a scientist experimenting with forces on wires carrying electric current. He was doing these experiments back in the 1820s, about the same time that Farday was working on Faraday’s Law. Ampere and Farday didn’t know that there work would be unified by Maxwell himself, about 4 decades later.

Forces on wires aren’t particularly interesting to me, as I’ve never had occassion to use the very complicated equations in the course of my work (which includes a Ph.D., some stints at a national lab, along with employment in the both defense and the consumer electronics industries). So, I’m going to start by presenting Ampere’s Law, which relates a electric current flowing and a magnetic field wrapping around it:

Equation [2] can be explained: Suppose you have a conductor (wire) carrying a current, *I*. Then this current produces a Magnetic Field which circles the wire.

The left side of Equation [2] means: If you take any imaginary path that encircles the wire, and you add up the Magnetic Field at each point along that path, then it will numerically equal the amount of current that is encircled by this path (which is why we write for encircled or enclosed current).

Let’s do an example for fun. Suppose we have a long wire carrying a constant electric current, *I*[Amps]. What is the magnetic field around the wire, for any distance *r* [meters] from the wire?

Let’s look at the diagram in Figure 1. We have a long wire carrying a current of *I* Amps. We want to know what the Magnetic Field is at a distance *r* from the wire. So we draw an imaginary path around the wire, which is the dotted blue line on the right in Figure 1:

Figure 1. Calculating the Magnetic Field Due to the Current Via Ampere’s Law.

Ampere’s Law [Equation 2] states that if we add up (integrate) the Magnetic Field along this blue path, then numerically this should be equal to the enclosed current *I*.

Now, due to symmetry, the magnetic field will be uniform (not varying) at a distance *r* from the wire. The path length of the blue path in Figure 1 is equal to the circumference of a circle of radius *r*: 2 x Pi x r.

If we are adding up a constant value for the magnetic field (we’ll call it *H*), then the left side of Equation [2] becomes simple:

Hence, we have figured out what the magnitude of the **H** field is. And since *r* was arbitrary, we know what the H-field is everywhere. Equation [3] states that the Magnetic Field decreases in magnitude as you move farther from the wire (due to the 1/r term).

So we’ve used Ampere’s Law (Equation [2]) to find the magnitude of the Magnetic Field around a wire. However, the **H** field is a Vector Field, which means at every location is has both a magnitude and a direction. The direction of the H-field is everywhere tangential to the imaginary loops, as shown in Figure 2. The right hand rule determines the sense of direction of the magnetic field:

Figure 2. The Magnitude and Direction of the Magnetic Field Around a Wire.

### Manipulating the Math for Ampere’s Law

We are going to do the same trick with Stoke’s Theorem that we did when looking at Faraday’s Law. We can rewrite Ampere’s Law in Equation [2]:

On the right side equality in Equation [4], we have used Stokes’ Theorem to change a line integral around a closed loop into the curl of the same field through the surface enclosed by the loop (*S*).

We can also rewrite the total current (I enclosed, I enc) as the surface integral of the Current Density (**J**):

So now we have the original Ampere’s Law (Equation [2]) rewritten in terms of surface integrals (Equations [4] and [5]). Hence, we can substitute them together and get a new form for Ampere’s Law:

Now, we have a new form of Ampere’s Law: the curl of the magnetic field is equal to the Electric Current Density. If you are an astute learner, you may notice that Equation [6] is not the final form, which is written in Equation [1]. There is a problem with Equation [6], but it wasn’t until the 1860s that James Clerk Maxwell figured out the problem, and unified electromagnetics with Maxwell’s Equations.

### Displacement Current Density

Ampere’s Law was written as in Equation [6] up until Maxwell. So let’s look at what is wrong with it. First, I have to throw out another vector identity – the divergence of the curl of any vector field is always zero:

So let’s take the divergence of Ampere’s Law as written in Equation [6]:

[Equation 8] |
---|

So Equation [8] follows from Equations [6] and [7]. But it says that the divergence of the current density **J** is always zero. Is this true?

If the divergence of **J** is always zero, this means that the electric current flowing into any region is always equal to the electric current flowing out of the region (no divergence). This seems somewhat reasonable, as electric current in circuits flows in a loop. But let’s look what happens if we put a capacitor in the circuit:

Figure 3. A Voltage Applied to A Capacitor.

Now, we know from electric circuit theory that if the voltage is not constant (for example, any periodic wave, such as the 60 Hz voltage that comes out of your power outlets) then current will flow through the capacitor. That is, we have **I** not equal to zero in Figure 3.

However, a capacitor is basically two parallel conductive plates separated by air. Hence, there is no conductive path for the current to flow through. This means that no electric current can flow through the air of the capacitor. This is a problem if we think about Equation [8]. To show it more clearly, let’s take a volume that goes through the capacitor, and see if the divergence of **J** is zero:

Figure 4. The Divergence of **J** is not Zero.

In Figure 4, we have drawn an imaginary volume in red, and we want to check if the divergence of the current density is zero. The volume we’ve chosen, has one end (labeled side 1) where the current enters the volume via the black wire. The other end of our volume (labeled side 2) splits the capacitor in half.

We know that the current flows in the loop. So current enters through Side 1 of our red volume. However, there is no electric current that exits side 2. No current flows within the air of the capacitor. This means that current enters the volume, but nothing leaves it – so the divergence of **J** is not zero. We have just violated our Equation [8], which means the theory does not hold. And this was the state of things, until our friend Maxwell came along.

Maxwell knew that the Electric Field (and Electric Flux Density (**D**) was changing within the capacitor. And he knew that a time-varying magnetic field gave rise to a solenoidal Electric Field (i.e. this is Farday’s Law – the curl of E equals the time derivative of **B**). So, why is not that a time varying **D** field would give rise to a solenoidal **H** field (i.e. gives rise to the curl of **H**). The universe loves symmetry, so why not introduce this term? And so Maxwell did, and he called this term the *displacement current density*:

[Equation 9] |
---|

This term would “fix” the circuit problem we have in Figure 4, and would make Farday’s Law and Ampere’s Law more symmetric. This was Maxwell’s great contribution. And you might think it is a weak contribution. But the existance of this term unified the equations and led to understanding the propagation of electromagnetic waves, and the proof that all waves travel at the same speed (the speed of light)! And it was this unification of the equations that Maxwell presented, that led the collective set to be known as Maxwell’s Equations. So, if we add the displacement current to Ampere’s Law as written in Equation [6], then we have the final form of Ampere’s Law:

[Equation 10] |
---|

And that is how Ampere’s Law came into existance!

### Intrepretation of Ampere’s Law

So what does Equation [10] mean? The following are consequences of this law:

- A flowing electric current (
**J**) gives rise to a Magnetic Field that circles the current

- A time-changing Electric Flux Density (
**D**) gives rise to a Magnetic Field that circles the**D**fieldAmpere’s Law with the contribution of Maxwell nailed down the basis for Electromagnetics as we currently understand it. And so we know that a time varying

**D**gives rise to an**H**field, but from Farday’s Law we know that a varying**H**field gives rise to an**E**field…. and so on and so forth and the electromagnetic waves propagate – and that’s cool.

### This website is educational. Materials within it are being used in accord with the Fair Use doctrine, as defined by United States law.

§107. Limitations on Exclusive Rights: Fair Use

Notwithstanding the provisions of section 106, the fair use of a copyrighted work, including such use by reproduction in copies or phone records or by any other means specified by that section, for purposes such as criticism, comment, news reporting, teaching (including multiple copies for classroom use), scholarship, or research, is not an infringement of copyright. In determining whether the use made of a work in any particular case is a fair use, the factors to be considered shall include:

the purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes;

the nature of the copyrighted work;

the amount and substantiality of the portion used in relation to the copyrighted work as a whole; and

the effect of the use upon the potential market for or value of the copyrighted work. (added pub. l 94-553, Title I, 101, Oct 19, 1976, 90 Stat 2546)

## Fuses

Fuses

### You can use adapters to turn one outlet into two… two outlets into four, and so on. What happens if you turn on all the devices connected to all these cords at once? They draw a lot of current through the wires to that outlet – and those wires can overheat, and start an electrical fire.

### Electrical fire

### This is why we need something in the house which can detect abnormally high electrical currents – and cut them off.

### Circuit breakers and fuse boxes.

### Here we see what could be a potentially fatal accident – a wet electrical appliance could conduct enough electricity to kill a person. How can we avoid this?

### “A ground fault circuit interrupter (GFCI) or Residual Current Device (RCD) is a device that shuts off an electric power circuit when it detects that current is flowing along an unintended path, such as through water or a person.”- Simple Wikipedia

### A GFCI on a hair dryer.

Lab Measuring Voltage Current DC circuits

- Learn how to build a simple circuit, measure voltage, and current
- Build a DC series circuit and DC parallel circuit

==========================

## The fuse

The fuse breaks the circuit if a fault in an appliance causes too much current flow. This protects the wiring and the appliance if something goes wrong. The fuse contains a piece of wire that melts easily. If the current going through the fuse is too great, the wire heats up until it melts and breaks the circuit.

Fuses in plugs are made in standard ratings. The most common are 3A, 5A and 13A. The fuse should be rated at a slightly higher current than the device needs:

- if the device works at 3A, use a 5A fuse
- if the device works at 10A, use a 13A fuse

Cars also have fuses. An electrical fault in a car could start a fire, so all the circuits have to be protected by fuses.

## The circuit breaker

The circuit breaker does the same job as the fuse, but it works in a different way. A spring-loaded push switch is held in the closed position by a spring-loaded soft iron bolt. An electromagnet is arranged so that it can pull the bolt away from the switch. If the current increases beyond a set limit, the electromagnet pulls the bolt towards itself, which releases the push switch into the open position.

from http://www.bbc.co.uk/schools/gcsebitesize/science/edexcel_pre_2011/electricityworld/mainselectricityrev3.shtml

======================

## Additional resources

### How does a Residual Current Circuit Breaker Work?

### External resources

http://www.electronicsteacher.com/direct-current/physics-conductors-insulators/fuses.php

https://www.allaboutcircuits.com/textbook/direct-current/chpt-12/fuses/

https://en.wikipedia.org/wiki/Thermal_management_(electronics)

https://www.howequipmentworks.com/electrical_safety/

https://www.howequipmentworks.com/electricity_basics/

### ===========================================

## Learning Standards

**Massachusetts 2016 Science and Technology/Engineering (STE) Standards
**

HS-PS2-9(MA). Evaluate simple series and parallel circuits to predict changes to voltage, current, or resistance when simple changes are made to a circuit

HS-PS3-1. Use algebraic expressions and the principle of energy conservation to calculate the change in energy of one component of a system… Identify any transformations from one form of energy to another, including thermal, kinetic, gravitational, magnetic, or electrical energy. {voltage drops shown as an analogy to water pressure drops.}

HS-PS3-2. Develop and use a model to illustrate that energy at the macroscopic scale can be accounted for as either motions of particles and objects or energy stored in fields [e.g. electric fields.]

HS-PS3-3. Design and evaluate a device that works within given constraints to convert one form of energy into another form of energy.{e.g. chemical energy in battery used to create KE of electrons flowing in a circuit, used to create light and heat from a bulb, or charging a capacitor.}

## Power (electrical)

If you look carefully at a stereo, hair dryer, or other household appliance, you find that most devices list a “power rating” that tells how many watts the appliance uses. In this section you will learn what these power ratings mean, and how to figure out the electricity costs of using various appliances.

The three electrical quantities

We have now learned three important electrical quantities:

Paying for electricity

Electric bills sent out by utility companies don’t charge by the volt, the amp, or the ohm. You may have noticed that electrical appliances in your home usually include another unit – the watt. Most appliances have a label that lists the number of watts or kilowatts. You may have purchased 60-watt light bulbs, or a 900-watt hair dryer, or a 1500-watt toaster oven. Electric companies charge for the energy you use, which depends on how many watts each appliance consumes in a given month.

A watt is a unit of power

The watt is a unit of power. Power, in the scientific sense, has a precise meaning. Power is the rate at which energy is flowing. Energy is measured in joules. Power is measured in joules per second. One joule per second is equal to one watt. A 100-watt light bulb uses 100 joules of energy every second. Where does the electrical power go?

Electrical power can be easily transformed into many different forms. An electric

motor takes electrical power and makes mechanical power. A light bulb turns electrical power into light and a toaster oven turns the power into heat. The same unit (watts) applies to all forms of energy flow, including light, motion, electrical, thermal, or many others.

Power in a circuit can be measured using the tools we already have. Remember

that one watt equals an energy flow of one joule per second.

Amps = flow of 1 coulomb of charge per second

Volts = an energy of 1 joule of energy / coulomb of charge

If these two quantities are multiplied together, you will find that the units of

coulombs cancel out, leaving the equation we want for power.

Watts equal joules/second, so we can calculate electrical power in a circuit by

multiplying voltage times current.

# P = VI

power measured in watts; voltage in volts; current in amps

A larger unit of power is sometimes needed.

A 1500-watt toaster oven may be labeled 1.5 kW.

kilowatt (kW) is equal to 1000 watts, or 1000 joules per second.

Horsepower – another common unit of power often seen on electric motors

1 horsepower = 746 watts.

Electric motors you find around the house range in

size from 1/25th of a horsepower (30 watts) for a small electric fan to 2 horsepower (1492 watts) for an electric saw.

## Virtual lab: Series and Parallel circuits

### Learn about electrical circuits with the PhET Circuit construction kit

* Briefly play with the app, learning the drag-and-drop components

* Follow the instructions. Carefully write answers in your notebook.

* Accurately answer questions in complete sentences, at a high school level.

**This must be completed in class to get credit. Unless you have an excused absence, you can’t make up the lab.**

### Learning Goals:

Develop a general rule regarding how resistance affects current flow,

when the voltage is constant.

Learn how changing resistance values affect current flow in both series and parallel circuits.

### Series Circuit A

Right click on the resistor, change the value of the resistor and observe what happens to the rate that the electrons move through it. The rate at which the electrons move is called current. Current is measure in Amps

(A) Make a general rule about the relationship between current and resistance.

– 10 points for circuit and accurate answer.

——————-

### Parallel Circuit B

Make observations & draw conclusions. – By right clicking on the resistors, change the values of the resistors, making one very high and one very low and visa versa.

Look for what happens to the current flow through the different resistors.

With regards to circuit B:

(a) Describe current at different locations in the circuit, esp. rate of the current and the value of the resistors.

(b) Explain your observations of the current flow in terms of the water tank model of electricity given to you in class

(c) Describe how your general rule from step 2 relates to your observations

– 20 points for circuit and accurate answer.

______________________________

### Circuit C

Change the values of the resistors, making one very high and one very low, and visa versa.

(a) Look for what happens to the current flow through the different resistors.

(b) Describe current at different locations in the circuit.

(c) Explain observations of the current flow in terms of the water-flow analogy.

(d) Describe how your general rule from the beginning relates to your observations.

Water flow analogies for electrical current

– 20 points for circuit and accurate answer.

=============================================================

### Circuit D: voltage in a series circuit

Build the series circuit shown below. On the left-hand menu, click voltmeter. You can drag-and-drop the red and black leads.

*In your notebook, add the following definitions:*

A **lead** is an electrical connection that comes from some device. Some are used to transfer power; ours are used to probe circuits.

A **multimeter** is a measuring instrument that combines multiple meters (measuring devices) into one Typical multimeters include

**ammeter** = measures **I **(current)

metric unit of current is **amperes (A)**

**ohmmeter** = measures **r** (resistance)

metric unit of resistance is **ohms (Ω)**

Ω is the Greek letter omega.

**voltmeter** = measures **v** (voltage) in a battery,

or the voltage drop across a part of a circuit.

metric unit of voltage is the **volt (v).**

With the knife-switch **closed**, what is the voltage drop across:

- the battery
- the light bulb
- the knife-switch
- the resistor

With the knife-switch **open**, what is the voltage drop across:

- the battery
- the light bulb
- the knife-switch
- the resistor

### ____________________________

### Circuit E: voltage in a parallel circuit

Build the series circuit shown below. On the left-hand menu, click voltmeter.

You can drag-and-drop the red and black leads.

What is the voltage drop across:

- the 2 batteries
- the resistor in the middle
- the light-bulb
- Points A and B on the wires.

=============================================================

### Circuit F: Measuring both I and V

Build the circuit shown here. Use the voltmeter to measure voltage, and the ammeter to measure current. Carefully fill in the 2 data tables. After you have taken the data, answer

(a) Compare the voltage numbers before you changed the resistance, to after you changed the resistance.

(b) Look just at the left column (default values) for current. Compare your numbers, to their locations on the circuit: What’s the relationship between the amount of current in one part of the circuit, to another? (Thinking of the water-flow analogy may be helpful.)

(c) Look at the right column for current. How did changing the value of one resistor affect the circuit (if at all?)

## Learning Standards

**Massachusetts 2016 Science and Technology/Engineering (STE) Standards**

HS-PS2-9(MA). Evaluate simple series and parallel circuits to predict changes to voltage, current, or resistance when simple changes are made to a circuit.

Technology/Engineering Progression Grades 9-10

The use of electrical circuits and electricity is critical to most technological systems in society. Electrical systems can be AC or DC, rely on a variety of key components, and are designed for specific voltage, current, and/or power.

## PhET Electric circuit lab

An electronics kit in your computer! Build circuits with resistors, light bulbs, batteries, and switches. Take measurements with the realistic ammeter and voltmeter. View the circuit as a schematic diagram, or switch to a life-like view.

### Learning Goals

- Discuss basic electricity relationships.
- Build circuits from schematic drawings.
- Use an ammeter and voltmeter to take readings in circuits.
- Provide reasoning to explain the measurements and relationships in circuits.
- Discuss basic electricity relationships in series and parallel circuits.
- Provide reasoning to explain the measurements in circuits.
- Determine the resistance of common objects in the “Grab Bag.”

PhET Circuit construction kit lab!

### Start with “*grab a wire*” – Pull a “wire” onto the screen.

### Add resistors, at least one battery, a lightbulb and a switch.

### Move the elements close together, so they connect.

### If you need to break 2 pieces apart, right click at the location, and choose ‘split junction’

### a) Create a series circuit with one light bulb that you can turn on/off.

### Click ‘voltmeter’ and a virtual voltmeter appears on the screen. Move the voltmeter’s **leads.**

### When the switch is off

### 1) measure the voltage across the bulb : _____

### 2) measure the voltage across the battery: _____

### Then with the switch on, do this again.

### b) Create a parallel circuit with 2 bulbs that you can turn on/off

### Click ‘voltmeter’ and a virtual voltmeter appears on the screen. Move the voltmeter’s **leads.**

### When the switch is off

### 1) measure the voltage across bulb A : _____

### 2) measure the voltage across bulb B : _____

### 3) measure the voltage across the battery: _____

### Then with the switch on, do this again.

## Kirchoff’s laws

### Kirchhoff’s laws are rules for understanding the behavior of electric current (I) and potential difference (V) in electrical circuits. They were first described in 1845 by German physicist Gustav Kirchhoff.

### They are widely used in electrical engineering and physics; we’re studying them in class now. The ideas behind them can be found in chapter 35 of Conceptual Physics (Hewitt/Pearson) Here is Kirchoff’s voltage law:

### Our presentation on this topic is here

https://kaiserscience.wordpress.com/physics/electromagnetism/electric-currents/