Curriculum

This page is read only. You can view the source, but not change it. Ask your administrator if you think this is wrong.
====== Electricity ======

prerequisite: [[Electrochemical Reactions]]

Three most basic quantities of electricity are:
  * current
  * voltage
  * resistance

^ quantity     ^ measured in ^ description                ^
| current I    | amps A      | flow (volume) of electrons |
| voltage V    | volts V     | force, pressure, or load   |
| resistance R | ohms Ω      | resistance to the flow     |

These three quantities can be measured with a multimeter.

===== Ohm's Law =====

Ohm's Law defines the relationships among these three quantities.

\begin{align}
voltage &= current * resistance \\
V &= I * R \\
volts &= amps * ohms \\
V &= A * Ω \\
\end{align}

Examples:
  * For a motor with a given resistance, increasing the voltage will increase the current.
  * If you want to increase the current to the motor, increase the voltage.
  * If you choose a motor with a higher resistance, the voltage must be increased to achieve the same current.
  * As the resistance is increased, the voltage must be increase to maintain the same current.


=== Human body sensitivity to electricity ===

Internal resistance between the ears is 100 ohms.

From finger to toe, 500 ohms.

More resistance, more current.  

A current of 0.1 amp for 2 seconds can be fatal.

A human has been killed at as low as 42 volts.

Hanging on a wire vs touching the wire and the ground.

^ Current      ^ Reaction                                                  ^
| 1 mA         | Faint tingle.                                             |
| 5 mA         | Slight shock.  Disturbing.  Most people can let go.       |
| 6-30 mA      | Painful shock.  Loss of muscular control.                 |
| 50-150 mA    | Extreme pain.  Cannot let go.  Death is possible.         |
| 1000-4300 mA | Ventricular fibrillation. Nerve damage.  Death is likely. |
| 10,000 mA    | Cardiac arrest.  Severe burns.  Death is probable.        |

Wet skin - 1000 ohms

Dry skin - 500,000 ohms

Length of time.  1 tenth of an amp, 100 mA, for 2 seconds can be fatal.

The human body is an eletro-chemical-mechanical device.
A nerve is a kind of conductor.
Muscles contract in response to an electrical stimulus.



===== Current =====

current - flow of electric charge 

electric charge flows when there is voltage present across a conductor

current is measured in amps

current can also be measured as electrons per second

one electron has a charge of 1.602e-19

one ampere = one coulomb per second

one coulomb = 6.242e+18 electrons

one ampere =  6.242e+18 electrons per second

===== Voltage =====

voltage is the force or pressure that causes current to flow in a circuit

voltage is measured in volts

the resistance of a conductor is the opposition to the passage of a current through that conductor

electric charge flows when there is voltage present across a conductor

"voltage present across a conductor"

"flow in a circuit"

"electric charge"1 

===== Resistance =====

resistance is measured in ohms

voltage forces charge to flow in a conductor, resistance opposes that force
2
===== Power =====

A fourth quantity, power, measured in watts, is a combination of current and voltage.

\begin{align}
power &= voltage * current \\
P &= V * I \\
watts &= volts * amps \\
W &= V * A \\
\end{align}

Power is a combination of the force and speed of electrons.

A household lightbulb can be defined by wattage, because household current is a given.  In Europe and Asia it is 220VAC.

So a 60 watt light bulb will pull $60w / 220v = .27 amps$.

===== Capacitor, Inductor, Resistor =====

The three elementary electrical components:
  * capacitor
  * inductor
  * resistor

More:
  * transformer
  * relay
  * switch

==== Capacitor ====

A capacitor has two plates separated by a space.
{{https://cdn1.iconfinder.com/data/icons/capatitors/100/electronic_component_capatitor-01-512.png?40}}

Each plate has area $A$.  The plates are separated by distance $d$.

Between the plates is a dielectric material (not to be confused with dialectic).

A dielectric material is an insulator that can be polarised by an electric field.  The electrons in the dielectric material cannot drift through the material, but they can shift slightly, causing dielectric polarisation.

The dialectic material has a dialectic constant $ε$.

Wires from a power supply are connected to the plates so that one is positive and the other is negative.

An electric field arises between the plates.

The electric field is measured in volts per meter $V / m$.

Electrical energy is stored in the field.

flux capacity

inductor, induce


==== Capacitance ====

The capacitance of a capacitor indicates how much charge the capacitor can store.

Capacitance is measured in farads (F) or microfarads (mF), named for Michael Faraday.


===== Inductance =====

An inductor is a coil.
{{ https://cdn1.iconfinder.com/data/icons/electronic-components-1/100/electronic_component-33-512.png?40}}

The coil is wound around a core of dielectric material.

A linear coil is called a solenoidal inductor.

===== Frequency =====



===== Projects =====

electric “train” made of battery, magnets, coil
https://youtu.be/J9b0J29OzAU 
 

===== Electricity vs Electronics =====

electrical circuit - controlled by mechanical switches

electronic circuit - controlled by electronic signals

===== Electrical Components =====

==== Wire =====

Wire can be distinguished by size and length.

There are three ways to denote the size of a wire.
  - by gauge, per American Wire Gauge (AWG). (bigger gauge : thinner wire)
  - by diameter, measured in mm
  - by cross-sectional area, measured in $mm^2$, used in EU countries

This wire size chart compares the three systems.
https://docs.google.com/spreadsheets/d/1rTeLpV_CcZR8-DhbEExSx8_EGOr-80V_An1KQbldgYc/edit#gid=1590490442

Calculate cross-sectional area from diameter with this equation:
$$ A = \frac{D^2 * pi}{4}$$

For wires made of bundled strands, use the same equation but multiply by n numbers of strands.

==== Diode =====

Light Emitting Diode (LED)

==== Generator ====

Convert motive power into electrical power.

The first generators were built in the 1830's.

Several types:
  * dynamo - uses a commutator to flip the AC to DC, generating a pulsing DC current.
  * magneto - generates AC current using permanent magnets
  * alternator - generates AC current using field coils

==== Commutator ====

A metal ring split into two halves, with an electrode attached to each halve.
Used in motors and in generators.

==== Motor as Generator ====

Regenerative braking - Electric vehicles use the motor as a generator to recharge the battery.

===== Electronic Components =====

==== Transistor ====

replaced vacuum tube

Types of transistor:
  * field effect transistor (FET)
    * metal-oxide-semiconductor FET (MOSFET) - most widely used type
  * bipolar junction transistor (BJT)

====== Electromagnetism ======

Force (physics)
  * mechanical linear
  * mechanical rotational
  * electrical 
  * magnetic


inductance
reluctance = resistance
conductance

flux
force

magnetomotive force vs flux

reluctance = ratio of force to flux in a circuit


circuit, field

reluctance
impedance
inductance


reluctance R = F / flux ϕ
It is sometimes known as Hopkinson's law and is analogous to Ohm's Law with resistance replaced by reluctance, voltage by MMF and current by magnetic flux.

permeance, the reciprocal of reluctance, P = 1/R

in electromagnetism, permeance is the inverse of reluctance
a magnetic circuit
   acts as though flux is conducted
   permeance is larger for a larger cross-section of material

in electricity, conductance is the inverse of resistance
an electric circuit
    conductance and resistance
    
-----

Triboelectric effect and charge
https://www.khanacademy.org/science/physics/electric-charge-electric-force-and-voltage/charge-electric-force/v/triboelectric-effect-and-charge?modal=1

balloon rubbed on the hair, electrons are moving from hair to balloon
hair becomes positive, balloon becomes negative

lightening

rubber shoes on carpet, touch doorknob

"charge"
positive, negative
opposite attract, like repel
framework, model
protons, electrons

e = charge of a proton
-e = charge of an electron

coulomb
1C ~= 6.24 * 10^18e
e = 1.60 * 10^-19C    reciprocal

==== Coulomb's Law ====

https://www.khanacademy.org/science/physics/electric-charge-electric-force-and-voltage/charge-electric-force/v/coulombs-law?modal=1

1785 Charles Augustin de Coulomb

Coulomb's law of electrostatic force

\begin{align}
F_e &= K_e \frac{|q_1q_2|}{r^2} &&\text{electrostatic force}\\
\text{where:}\\
q_1 &= \text{charge 1} \\
q_2 &= \text{charge 2} \\
r &= \text{distance between charges} \\
K_e &~= 8.987551 * 10^9   * Nm^2 / C^2    &&\text{electrostatic constant} \\

&&&\text{resulting units Newton meter squared / coulomb squared} \\
\end{align}

Analogous to Newton's Law of Gravity

\begin{align}
F_G &= G m_1 m_2 / r^2       &&\text{force of gravity} \\
G &~= 6.674×10^−11 m^3⋅kg^−1⋅s^−2 &&\text{gravitic constant} \\
\end{align}


q_1 &= +5 * 10^3 C \\
q_2 &= -1 * 10^-1 C \\
r &= 0.5m \\
\end{align}

==== Circuit ====
voltage drop across a component \\
the entire voltage is dropped across the whole circuit \\
resistors wired in series share the voltage drop proportionate to the resistance in ohms \\

==== AC generator types ====
  * standard - produce electricity in a single phase
  * invertor - produce electricity in three phases, invert to DC, invert back to more stable 
  * AC
  * induction (asynchronous) - 
  * synchronous - 
  * brushed - produce AC with sine wave fairly close to grid wave
  * brushless - use electromagnetic induction instead of mechanical brushes


==== generator vs motor ==== 

mirror image
                 
==== Motor Types ====                      
  * induction
  * brushed
  * brushless
  * AC 
  * DC 
  * single phase
  * 3-phase


==== Battery Chemistry ====

any two different kinds of metal can be placed in a conducting solution and you get a battery. 

copper and zinc strips into a lemon or a potato

soda can, the soda from the can, and some copper.

Zinc copper soda

https://en.m.wikipedia.org/wiki/Battery_balancing
Battery balancing and battery redistribution refer to techniques that improve the available capacity of a battery pack with multiple cells (usually in series) and increase each cell's longevity.[1] A battery balancer or battery regulator is an electrical device in a battery pack that performs battery balancing.[2] Balancers are often found in lithium-ion battery packs for laptop computers, electrical vehicles. etc.

state of charge (SOC)

Balancing is only necessary for packs that contain more than one cell in series. 

Parallel cells will naturally balance since they are directly connected to each other, 

but groups of parallel wired cells, wired in series (parallel-series wiring) must be balanced between cell groups.

Active balancing passive balancing

Bottom balancing top balancing

Balancing while not charging

https://youtu.be/OjGAvbULBH8
Battery pack with BMS made for three lithium ion cells
Thin wires for balancing thick wires for carrying current

Thickness 0.10, 0.12, 0.15, 0.20 mm
Width 5, 8, 10 mm

Student make battery
https://sciencing.com/making-wet-cell-battery-4781656.html

AC vs DC: ohm's law applies equally unless there is a capacitance or an inductance in the circuit.

Faraday
Lenz
Franklin

Voltage drop
http://wiresizecalculator.net/calculators/voltagedrop.htm

Inductor ac vs dc
https://www.homemade-circuits.com/inductors-in-acdc-circuits-explained/

induction = asynchronous
an induction motor can be used as a generator and vice-versa
an induction machine is both a generator and a motor
induction is for AC only
is induction always three-phase AC?
1. start with induction motor attached to the AC input line
2. apply a torque to the rotor to bring it up to match the speed of AC input line, the synchronous speed, current falls to zero
3. speed up the rotor past the synchronous speed, reverse current is generated

synchronous and induction generators are both alternators


https://www.homemade-circuits.com/inductors-in-acdc-circuits-explained/

inductors and capacitors are often used together. they are complementary.

inductor and capacitor and battery all store electric energy

inductor stores energy in the form of magnetic energy

inductor capacitor
inductor | initial energy stored | energy released after |
capacitor | energy stored gradually | when is energy released?

an inductor in AC == a resistor in DC

inductor 
in DC: behave and produce a short across inself
in AC: offer an opposing or restricting response, aka "choke"

suppressing high frequencies, suppressing surge currents, for bucking or boosting voltages

inductance: the property of opposiing instantaneous current 
reactance: the magnitude of this opposing force, proportional to frequence and current

made of coils or turns of wire


https://theelectronicshobbyblog.com/2019/03/25/beginners-corner-inductors-in-dc-circuits/

inductor - stores energy in a magnetic field
capacitor - stores energy in an electric field


https://electronicsphysics.com/faradays-law-of-electromagnetic-induction-for-emf/
this author uses the verb "induce" incorrectly

Oersted: current carrying wire produces magnetic field around it
Biot-Savart law, Ampere's circuital law, Fleming's right hand thumb rule, Maxwell's corkscrew rule

the reverse is also true

a current is induced in a conductor in a varying magnetic field 
Faraday's law of electromagnetic induction
induced EMF
electromotive force (EMF)
the EMF can drive a current

faraday law 1
Whenever a conductor is placed in a varying magnetic field, an electromotive force is induced. If the conductor circuit is closed, a current is induced, which is called induced current.
Note: the EMF is a potential.  The current is actual.

faraday law 2 - calculate the magnitude of the induced EMF
e = N × dΦ / dt

Lenz's Law
e = -N × dΦ / dt
Add minus sign.  The polarity of induced EMF is such that it would produce a current which opposes the change in magnetic flux that produced it.
Φ =  change in magnetic flux
t = time
N = Number of turns
e = EMF

flux -> change in flux -> EMF\\
https://youtu.be/Y2XvIofbwpc



electromagnetic induction
https://en.wikipedia.org/wiki/Electromagnetic_induction
directly proportional to number of turns/coils in the conductor
variance.  moving the field or the conductor.  using AC. 

analogies	
Lenz's law may be seen as analogous to Newton's third law in classical mechanics[2][3] and Le Chatelier's principle in chemistry.[4]

laws: qualitative vs quantitative (equation ?)

difference between magnetic and electric circuit
https://circuitglobe.com/difference-between-magnetic-and-electric-circuit.html
table
^ magnetic circuit             ^ electric circuit                    ^
| magnetic flux                 | electric current                   |
| flux = mmf / reluctance | current = emf / resistance  |
| mmf                               |  emf                                    |
| reluctance                     | resistance                             |
| current                           | flux                                      |
| permeance                    | conduction                          |
| permeability                  | conductivity                         |
| reluctivity                       | resistivity                             |
| flux density                    | current density                    |
| magnetic intensity         | electric density                   |
| mmf drop                       | voltage drop                       |
| nothing flows                 | electrons flow                     |
| no insulators                  | many perfect insulators      |
| reluctance is not constant | resistance is almost constant |
| magnetic lines of flux flow from north to south | electric current flows from positive to negative |


AC to DC
Rectifier plus capacitor

Tesla 
model S
induction motor
conventional well-proven 
Squirrel cage rotor
3% inefficiency
Model 3
Ipm sim rm
Magnetic and reluctance action
Four permanent magnets on rotor
RMF rotating magnetic field, can be DC 2 phase or three phase
PM motor
Good starting torque
Back EMF at high speeds
Synchronous reluctance motor SynRM
Good at high speeds, No back EMF 

Combined PM and SynRM

3 phase ac power to the stator
Produces a rmf
A 4 pole Rmf
Induces current on the rotor bars

In an induction motor
The rotor speed always lags behind the rmf
Rotor speed < rmf speed

No brushes
No permanent magnets
Speed depends on the frequency of the ac power supply
Variable frequency drive - controls motor speed
From 0 to 18,000 RPM

Jan 14 10 am

three-phase induction motor - has three separated pairs of coils in the stator

The stator generates an RMF.

The shaft is connected to the rotor.

Squirrel cage rotor - Two end rings connected by some bars, resembling a hamster wheel.

The squirrel cage is effectively a set of wire loops.  The RMF generated by the stator induces a current in each of the wire loops of the squirrel cage.  The current in each wire loop generates a magnetic field. This magnetic field in the rotor interacts with the magnetic field in the stator resulting in rotation.

Induction, four types

electrostatic - a redistribution of electric charge in an object, caused by the influence of nearby charges

Electromagnetic induction - Current in a wire generates/produces/creates/induces a magnetic field around the wire.

Electric induction - a changing magnetic field induces a current in a nearby conductor.

Magnetic induction - is the process of magnetization of materials in an external magnetic field. (Same as electrostatic ?)


One of the four fundamental forces in the universe is the electromagnetic force. Not the electrical force or the magnetic force, but the electromagnetic force.

Can a battery drive a three-phase ac motor?

In north America, split phase system.

Variable frequency drive (VFD)
Rectifier - 3 phase ac to pulsed dc, 6 diodes
DC bus - smooth dc, capacitor
Inverter - DC to ac pwm, igbt's 

Insulated-gate bipolar transistor - 
https://m.youtube.com/watch?v=yEPe7RDtkgo

Potentiometer - variable resistor

PWM
Control lighting 
control motor speed 
create efficient power supplies

Also used to send data
Tv remote control

Also used in audio amplifiers
99% efficient, as opposed to 25 to 50% efficiency of non pwm amplifiers

Switching frequency
Duty cycle

Average voltage, perceived power

Use PCM to control lighting
The flicker fusion rate in the human brain is 18 times per second
Frequency 100 times per second
Duty cycle 25%

Older systems use DC voltage control
By placing a variable resistor in the circuit
Excess energy wasted as heat, always the same current regardless of dimming
More narrow range of variability
Smoother power delivery


The PCM used for servos is different
Position of a servo
Acceleration of an esc

Between 1000 and 2000 microseconds

555 IC

The pulse wave is a square wave meaning it has a low and a high value meaning it can be used to represent binary data.

Torque ripple

Applications
Rooftop ventilation fan
Elevator
Drone propeller
Electric motorcycle
Robotic elbow
DIY generator
DIY motor

Rectifier | ac to dc
Inverter | DC to ac
Transformer | ac to ac
Converter | DC to DC

Any motor becomes a generator if you spin it.

AC and DC generators, animation
https://www.khanacademy.org/science/in-in-class-12th-physics-india/in-in-electromagnetic-induction/x51bd77206da864f3:ac-generator/v/ac-dc-generator
brushes and slip rings = AC generator
brushes and split rings = commutator = DC generator

three phase generator, motor
six wires I get, three wires, 9 wires, 12 wires I don't get


https://m.youtube.com/watch?v=K8Ir1-COjnc&t=0s
In a balanced three phase generator the fourth wire the neutral wire will have zero current and therefore it can be removed.


radial flux vs axial flux - orientation of the coil windings in the stator


Bldc and pmsm are both synchronous and both use permanent magnets

permanent magnet Synchronous machine (PMSM)

Differentiation: shape of back emf voltage

==== Light Emitting Diode (LED) ====

https://components101.com/diodes/5mm-round-led

Anode - Positive terminal of LED

Cathode - Negative terminal of LED

symbol

direction of current

^ LED Color ^ Forward Voltage ^ 
| Red       | 1.63 ~ 2.03V    |
| Yellow    | 2.10 ~ 2.18V    |
| Orange    | 2.03 ~ 2.10V    |
| Blue      | 2.48 ~ 3.7V     |
| Green     | 1.9 ~ 4.0V      |
| Violet    | 2.76 ~ 4.0V     |
| UV        | 3.1 ~ 4.4V      |
| White     | 3.2 ~ 3.6V      |


==== Applications ====
  * Elevator (industrial)
  * Drill ac (household)
  * Drill dc
  * Quadcopter
  * Motorcycle
  * Car

servo - robotic elbow

stepper - 

==== Instruments ====

Multimeter

Oscilloscope

Clamp Meter


==== EMF ====

voltage vs emf vs flux
https://www.khanacademy.org/science/in-in-class-12th-physics-india/in-in-electromagnetic-induction/x51bd77206da864f3:ac-generator/v/emf-flux-equation-graph-of-ac-generator

====  motor types ====


there is no such thing as a dc motor

Servo =
DC motor
Gear box
Potentiometer
Circuit board

Gearbox step down rpm, increase torque
Output of gearbox connects to potentiometer
Closed loop - potentiometer turns 180 degrees
Open loop - potentiometer turns 360 degrees


Syllogism vs dialectic

==== Magnet ====

Eletromagnet vs permanent magnet.

Often a permanent magnet is painted, \\
so the south pole is blue, \\
and the north pole is red.

South pole is positive.\\
North pole is negative.

Earth's north is actually south

| north | red  | negative | Earth's south pole, antartic |
| south | blue | positive | Earth's north pole, artic    |

Electromagnet also has poles.\\
Fleming's right-hand-rule.\\
http://kitbook.com/electromagnet-poles/

battery plus to solenoid, wrap clockwise, starting at south pole, \\
https://www.youtube.com/watch?v=n63DAWvaHlk

letter N is counter-clockwise arrow symbol\\
look at the north pole of the magnet\\
current will be going thru the coil counter-clockwise\\

letter S is clockwise arrow symbol\\
look at the south pole of the magnet\\
current will be going thru the coil clockwise\\






===== Electricity =====

A generator produces AC.

A battery produces DC.

AC does not have positive and negative.

AC has hot and neutral.

| Alternating | AC | hot - neutral       | vibrating back and forth  | sine wave     | generator |
| Direct      | DC | positive - negative | continuous flow           | straight line | battery |



great animations of magnetic fields
https://www.youtube.com/c/Physicsandanimation

==== Direct Current (DC) ==== 

A battery has two terminals, positive and negative.
Between the two terminals is an electrolyte.

Chemistry.  A charged battery has a buildup of extra electrons at the negative terminal.

When a circuit is completed, the extra electrons flow from the negative terminal to the positive terminal, until the two terminals are balanced, and the battery has lost its charge. 

=== Conventional, Positive, Wrong ===

When scientists first started working with electricity, they did not know about protons and electrons.

making batteries, 

| electron        | negative to positive | correct        | electronic engineers |
| positive charge | positive to negative | "conventional" | electrical engineers |

Electronic engineers say electric current is the flow of electrons from negative to positive.

Stubborn electrical engineers say current is the flow of a positive "space" from positive to negative.  They call this "conventional" current or positive current.  I call this wrong.

Conciliatory persons say there are two simultaneous currents: negative bits flow one way, and positive bits flow the opposite way.

Consider a queue of persons waiting in line for ice cream.  When the person at the counter is served he moves away leaving a space.  The next person in line moves forward to the space at the counter, leaving a space behind him.  The person behind him steps forward to fill the space.  And so on with each person back to the end of the line.

In this example, what is moving: the people, or the space?

some of the excuses I have heard.
  * Too hard to change now.  Like telling Americans to drive on the left, there would be chaos.
  * It doesn't matter mathematically in circuit analysis.  (not true for batteries, transistors and diodes)
  * There are two simultaneous and opposite circuits: the electrons flow from negative to positive, the positive charge flows from positive to negative.  (False) 

Ben Franklin is often blamed for the mixup, because he described positive and negative charges 50 years before the first battery, and 150 years before the electron was discovered.

Animation of ice cream queue.
Circuit drawings: battery, LED.  Two drawings, electron and "conventional".

{{ ::queue_chair.mp4?loop | Electron Queue Analogy}}


right-hand rule\\
first-finger gives direction of the flux\\
second-finger gives direction of the current\\
which current is this?  electron or conventional
He decided that the glass rod being rubbed with silk would be a positive charge while the rubber and fur would be a negative charge. So, with that convention, by removing electrons, the glass rod became positively charged and by adding electrons, the rubber rod became negatively charged.



  * 1752 Ben Franklin flew his kite in a storm and captured electricity from lighting.  He described positive and negative charges.
    * Rubbing a glass rod with silk produces a positive charge.
    * Rubbing rubber with fur produces a negative charge.
  * 1800 Alessandro Volta invented the first battery, the voltaic pile. https://www.liquisearch.com/alessandro_volta/first_battery
    * zinc: negative electrode
    * copper: positive electrode
    * saltwater: electrolite
  * 1861 Maxwell presents his equations (right-hand thumb rule?)
  * 1897 J.J. Thomson discovers the electron, described it as a negatively charged particle floating in a sea of positive charge, like plums in a pudding, the "plum pudding model"
  * 1909 Rutherford discovers the nucleus in the gold foil experiments and develops the planetary model
  * 1913 Niels Bohr discovers the specific energy levels of electrons in the atom
  * 1940 US Navy begins training electronics engineers using the electron current.
  * 1945 John Ambrose Fleming dies


Battery\\
two terminals marked + and -\\
Is that true?  Does the - terminal really have a superfluence of electrons?
annode, cathode

chemical reactions:
  * oxidation = loss of electrons
  * reduction = gain of electrons

anion - has gained an electron, negative charge
cation - has lost an electron, positive charge

cathode - reduction occurs, 

anode - oxidation occurs, anions give off electrons, negative charge

species?

electrons flow from anode to cathode, from oxidation half to reduction half

inside the battery, electrons flow from positive to negative inside the battery
outside the battery, from negative to positive

flow is reversed by a battery charger, something with a bigger voltage

, AAA, AA, C, D dry cell

^ description    ^ anode (-)    ^ cathode (+)          ^ electrolyte                        ^
| zinc-carbon    | zinc         | manganese            | ammonium chloride or zinc chloride |
| alkaline       | zinc powder  | manganese dioxide    | potassium hydroxide (alkaline)     |
| lithium-ion    | carbon, graphite | lithium metal    | aquaeous salts                     |
| li-ion polymer | carbon, graphite | lithium cobalt oxide | polymer                        |
| lead-acid      | lead dioxide | metallic lead        | sulfuric acid                      | 

The electrolyte helps transport ions between positive and negative electrodes.
 


==== Alternating Current (AC) ==== 

===== Magnetic Field ===== 

==== Calculate and Plot a Magnetic Field ====

Numerical Error with Simulation...\\
https://physics.stackexchange.com/questions/139479/numerical-error-with-simulation-of-electric-charge-in-homogeneous-magnetic-field

Mathematical Model of Magnetic Field Lines\\
https://spacemath.gsfc.nasa.gov/earth/9Page23.pdf