# Electronics/Voltage

## Electric Field: E

A stationary charge has an electric field surrounding it given by:

$E A = Q/\epsilon_o$

A is 4 π r2 the surface area of a sphere
Q/εo is how much the electric field deforms space

This becomes:

$E = {Q \over 4 \pi r^2 \epsilon_o}$

## Permittivity: &epsilon

• Permittivity: (&epsilon) How much energy a material absorbs when subject to an electric field. Similar to stretching a spring, when the electric field is removed, the material gives up the energy it has absorbed.
• Vacuum Permittivity: The permittivity of the vacuum. &epsilono = 8.85419 10-12 F/m.
• Relative Permittivity: The permittivity of materials relative to the vacuum. Also known as the Dielectric Constant: &epsilonr. Where &epsilon is the permittivity of the material.
$\epsilon_{r} = \frac{\epsilon}{\epsilon_{0}}$
• Dielectric: Usually an insulator. Acts to decrease the strength of the electric field.
• Dielectric Strength: The maximum electric field a dieletric can handle before the electric field frees its bound electrons, turning the material into a conductor. The field strength at which breakdown occurs in a given case is dependent on the respective geometries of the dielectric (insulator) and the electrodes with which the electric field is applied, as well as the rate of increase at which the electric field is applied. Voltage is usually less than this number, and breakdown occurs when this number is exceeded.
• Birefringence: double refraction.
• Isotropic: behavior does not depend on direction.
• Anisotropic: behavior depends on direction.

## Voltage: V

The difference between two points in an electric field is the voltage V.

$V = E \Delta x$

Voltage is used in accelerators to accelerate charged particles to the speed of light. In Electronics voltage is the potential between two opposing charges given by:

$V = {q_1 \over 4 \pi \epsilon_o r_1} + {q_2 \over 4 \pi \epsilon_o r_2}$

Where &epsilono is the permittivity of the vacuum, q1 and q2 are the values of the two charges (in coulombs), and r1 and r2 are their distances. Note how the Voltage falls off as 1/r.

If the charges were similar it would not make any sense. But if the particles have opposite charges then the voltage connects the charges. Through voltage positive charges go to the negative end, and negative charges go to the positive end.

Voltage causes charged particles to move according to the rules of repulsion and attraction, so electrons move from negative to positive. Two charged particles have a potential between them that relates to their separation distance.

Charged particles separated by a distance have a voltage associated with them. If the particles have a similar charge the voltage is repulsive and does not mean much.

## Work: W

PE
A charged particle in an electric field at distance r has an electrical potential energy U associated with it.

$U = Q V$

KE
When a charged particle is place in an electric field at distance r it has a force on it. The direction of force depends on the two charges, but minimizes the PE.

$F = Q E$

Acceleration

When a charged particle moves due to the force of an electric field it does work. This work causes the particle to accelerate.

Work W is the change in U, or F applied at a distance.

$W = \Delta U = F \Delta x$

Falling downhill is positive work for the electric field and climbing uphill is positive work for the charged particle. Similar charges repel so bringing them together is uphill. Opposite charges attract so moving them apart is uphill.

## Current: I

So the voltage on a charged particle causes it to accelerate. This is known as current.

It is sometimes taught that current in electric circuits is composed of electrons, which flow from the negative terminal of the power source to the positive at the speed of light. This is not (completely) true.

1. Electricity is carried by charged particles.
This can mean any small particles that carry charge and are free to move. In metals, electrons are free to move and the metal nuclei are not. In salt water, however, electrons, negative ions, and positive ions are free to move, and do, when a voltage is applied (batteries and electrolytic capacitors are examples of electrical components that carry charge as ions). In your own nerve cells, electricity is carried by moving ions, such as potassium and sodium. In semiconductors, electricity is carried by electrons, but is often much more easily understood as movement of "holes"; the absence of an electron. In some static electricity experiments, electricity can be carried by charged dust or small pieces of paper.
2. Electrons drift through conductors.
• When you flip the light switch, the light comes on almost instantly. This does not mean that the electrons themselves move that quickly. In fact, they usually move much much slower. A typical speed for electron drift in a DC electronic circuit is slower than molasses. The electrons themselves are moving very quickly, but not in one direction. They are constantly moving randomly from atom to atom, and only have a very gradual drift, or shift in average position over time. The speed electrons drift actually depends on voltage, resistance of the conductor, shape of the conductor, material the conductor is made of, temperature, and other factors.
• What is actually traveling quickly is electromagnetic waves; the pushing of electrons by their neighbors. This is similar to the way a wave in water works. When you drop a stone in a pond, a wave spreads out from where the stone hit the surface. But does the water itself move? Not really. The water molecules at the surface are just moving back and forth, and their cumulative effect is the wave that you see, which travels in one direction. This is similar to the travel of an AC wave down a transmission line. (we could make a better analogy to waves of car traffic or waves of people in line for a ride at the fair) An interesting analogy would be moving a hand through air. The hand is the wave and the air is the random electron movement.
3. Electromagnetic waves only travel at the speed of light in a vacuum.
• What is usually meant when someone says "the speed of light" is actually "the speed of light in a vacuum", as light itself slows down while traveling through materials. A typical speed for a signal traveling down common coaxial cable is 2/3 the speed of light (in a vacuum). (This is about 200,000,000 m/s.) The wave traveling down the cable is actually the same thing as light, just at a different frequency. The waves traveling through your nerves as you read this are traveling at about 120 m/s.

As you increase voltage you increase the electric field and the speed at which charged particles travel. This is why increasing voltage directly increases current. Reversing the voltage reverses the current.

Sometimes you have voltage but no current. This is used in analog and digital circuits to control switches.

So, negative particles drift from negative to positive voltage, and positive particles drift in the opposite direction from positive to negative voltage. The particles drift at different speeds in different materials. speed of "holes" based on bandgap. Given the presence of holes we tend to ignore the particles and focus on the current flow. Current is measured by the amount of charge flow per unit time and represents the speed of the electromagnetics waves. In talking about current we will mainly talk about electrons flowing, as they are the predominant charge carriers in metal and many circuit components.

Current = flow of charge (usually electrons

Current is the change in charge over time.

$I={dQ \over dt}$

Accumulation of current is charge. Talk about cells and capacitors.

$Q=\int I dt$

## Resistance: R

Resistance opposes the flow of electrons. In the absence of resistance current shorts and flows unhindered like that of a power surge. Resistance combined with voltage set limits on the current that is allowed to flow through electronics. This is necessary otherwise the parts would melt (extreme electromigration). As resistance increases the flow of charge slows to a trickle until current stops flowing. Given the sheer number of electrons flowing this does not happen until resistance is effectively infinite.

Without resistance this is effectively a short meaning the electrons flow unhindered.

The current is limited by the voltage. Resistance stops the flow of current. A short circuit has no resistance. As resistance increases to infinity the current stops flowing and becomes an open circuit.


$I = {V \over R}$

This is known as Ohm's law. Which says that Current I is equal to Voltage V divided by Resistance R. Or that voltage creates current and resistance limits the flow of current. In a circuit resistance does not change much, so most of the behavior of a circuit depends on the voltage which controls the current.

Current through a conductor versus an insulator like air.