Circuits - 2

OK, so about regular circuits:

The images represent SERIES CIRCUITS and PARALLEL CIRCUITS.

In a series circuit, the current is constant and is set by the total resistance of the circuit (the sum of the resistors). If you remove one resistor (or light bulb, as in the first image), the current stops. If the resistors were identical bulbs, having more bulbs would result in dimmer bulbs, since the battery voltage is distributed among them.  Note that the sum of the voltages "over" the bulbs is equal to the total voltage provided by the battery (give or take some minor losses).  Identical bulbs (or resistors) have identical voltages "over" them - 3 identical bulbs connected to a 9-V battery would have roughly 3-V each over them.

In parallel circuits, current has multiple paths to take, so the total resistance of the circuit is actually LESS than if the resistors were alone or in series with other resistors - see details below. Since the bulbs are connected equally to the battery, they experience the same as the battery voltage - they are, therefore, of equal brightness (and the same brightness they would have if there were only ONE bulb connected). Of course, bulbs in parallel draw more current and thus cause a battery to die sooner.  You could have 10 bulbs or resistors connected in parallel to a battery - each will be as bright as if only 1 were connected to the battery (same voltage over each), though 10 bulbs will kill the battery 10 times faster.

Does this have anything to do with holiday lights?

What I've written above is primarily geared toward identical bulbs. In series, add up the resistances to get the total resistance. In parallel, it is more complicated. There is a formula one can use (1/Rp = 1/R1 + 1/R2 + ...), but we will only concern ourselves with the case of identical resistors in parallel. In that case, divide the value of the resistor by the number of resistors to get the total effective resistance. For example, two identical 50-ohm resistors in parallel is the same as one 25-ohm resistor. This seems strange, but it's a little like toll booths - when one toll booth is open, it can get crowded (the current is small). With multiple toll booths open, the resistance is effectively less, so the current can be greater.

In the first image below, the graphic represents the schematic view of a parallel circuits, with 2 resistors.  Note that 2 possible paths are available for current to take - current runs through EACH path, though there will be more current where there is less resistance.  The total current from the battery is equal to the sum of the currents through the 2 resistors.  It follows V = I R, though the V over each R is the same.  The I through each will therefore be V/R.

The second image illustrates the series circuit concept:  identical resistors in series will effectively give MORE resistance (the sum of the resistances, actually) to the battery, so the current will be LESS (and exactly the same in each resistor or bulb).  It also easily follows V = I R, with more R yielding less I (when V is constant).  Think of V = I R this way:  I = V/R.  More R, less I.

Bulbs in Series - same current through each, but the voltage from the battery "splits"

Bulbs in Parallel - same voltage over each, but the current from the battery "splits"

Introduction to Circuits

Thus far, we have only discussed "static" (stationary) charges.  Static charges alone are useful, but not nearly as much as charges in motion.  As you recall, electrons are the most easily moved particles.  However, for sake of ease in sign convention (positive vs. negative), we define the following:

Current (I) - the rate at which positive charge "flows"

I = Q/t

The unit is the coulomb per second, defined as an ampere (A).  Just as one coulomb is a huge amount of charge (nearly 6.3 billion billion protons), one ampere (or amp) is a tremendous amount of current - more than enough to kill a person.  In fact, you can feel as little as 0.01 A.  Typical currents in a circuit are on the order of mA (milliamperes).

Essentially, current is how quickly charge travels (or charge per time, q/t).  The unit (a coulomb per second) is called the ampere (or amp, A).  To keep things simple, we think about positive charge moving, even though it is really all about the electrons.

We need to define other new quantities in electricity:  voltage, resistance, power.

Voltage (V) - the amount of available energy per coulomb of charge.  The unit is the joule per coulomb, called a volt (V, in honor of Allesandro Volta, inventer of the battery).

V = E/Q

Batteries and other sources (such as wall sockets) "provide" voltage, which is really a difference between TWO points (marked + and - on a battery).  

Resistance (R) - the ratio of voltage applied to an electrical device to the current that results through the device.  Alternately:  the amount by which the voltage is "dropped" per ampere of current.

R = V/I

You can also think of resistance as that which "resists" current.  Typically, resistors are made of things that are semi-conductive (they conduct current, but less well than conductors and better than insulators).  Resistors are often made of carbon, but can also be made of silicon and other materials.  The unit is the volt per ampere, defined as an ohm (Greek symbol omega)

A convenient way to relate all of the variables is embodied in an expression often called Ohm's Law:

V = I R

So, what exactly IS a circuit?

An electrical circuit can be thought of as a complete "loop" through which charge can travel.  Therefore, it actually has to be physically complete - there can be no openings.  That is, the current actually has to have a complete path to take.  I will demonstrate this in class with bulbs and wires; for now, see the image above.

https://phet.colorado.edu/en/simulation/circuit-construction-kit-dc

What about power?

Also consider electrical power (P).  Power is the rate at which energy is used or expended:  energy per time.  Symbolically:  P = E / t.  The unit is the joule per second, called a watt (W).  In electricity, power is also given by:

P = I V

P = I^2 R

Power allows us to express the brightness of a bulb.  Consider that a 100-W bulb is brighter than a 60-W bulb.

Some folks like analogies.  Consider a water analogy.  Voltage is like a tank of water (how much water).  Resistance is provided by a drain or faucet.  The rate at which water comes out is the current.  It's only an analogy, but it gets the gist of circuit terminology ok.

Charge questions

Things to think about:

1.  What exactly *is* charge?  How do we think of it?  How does this relate to protons and electrons, etc.?

2.  Why is it that electrons are the easiest particles to manipulate?

3.  What does atomic number (Hydrogen = 1, Helium = 2, etc.) mean?

4.  What are quarks?

5.  Coulomb's law is an "inverse square law" - what does this mean exactly?

6.  Why can a charged balloon stick to a wall?

7.  What is "grounding"?

8.  Recall the demonstration where I charged up the small suspended piece - what was I showing?

Intro to electricity

Electricity Part 1 - Charge!

Charge

- as fundamental to electricity & magnetism as mass is to mechanics

Charge is a concept used to quantatively related "particles" to other particles, in terms of how they affect each other - do they attract or repel?  If so, with what force?

Charge is represented by letter Q.

The basic idea - likes charges repel (- and -, or + and +) and opposite charges attract (+ and -).

Charge is measured in units called coulombs (C).  A coulomb is a huge amount of charge, but a typical particle has a tiny amount of charge:

- the charge of a proton is 1.6 x 10^-19 C.  Similarly, the charge of an electron is the same number, but negative, by definition (-1.6 x 10^-19 C).  The negative sign distinguishes particles from each other, in terms of whether or not they will attract or repel.  The actual sign is arbitrarily chosen.

The charge of a neutron is 0 C, or neutral.


But what IS charge?

Charge is difficult to define.  It is property of particles that describes how particles interact with other particles. 

In general, the terms are negative and positive, with differing amounts of each, quantified as some multiple of the fundamental charge value (e):

e = 1.6 x 10^-19 C

That's hard to visualize, since a coulomb (c) is a huge amount of charge.  One coulomb, for example, is the charge due to:

1 coulomb = charge due to 6.3 x 10^18 protons

A typical cloud prior to lightning may have a few hundred coulombs of charge - that's an enormous amount of excess charge.

If the charge is negative (-), the excess charge is electrons.

If the charge is positive (+), the excess charge is protons - however, we can NOT easily move protons.  That usually takes a particle accelerator.  Typically, things are charged positively by REMOVING electrons, leaving a net charge of positive.

Other things to remember:

Neutral matter contains an equal number of protons and electrons.

The nucleus of any atom contains protons and (usually) neutrons (which carry no charge).  The number of protons in the nucleus is called the atomic number, and it defines the element (H = 1, He = 2, Li = 3).

Electrons "travel" around the nucleus in "orbitals."  See chemistry for details.  The bulk of the atom is empty space.

Like types of charge repel.  Opposite types of charge attract.

The proton is around 2000 times the mass of the electron and makes up (with the neutrons) the bulk of the atom.  This mass difference also explains why the electron orbits the proton, and not the other way around.

Protons in the nucleus of an atom should, one would imagine, repel each other greatly.  As it happens, the nucleus of an atom is held together by the strong nuclear force (particles which are spring-like, called gluons, keep it together).  This also provides what chemists called binding energy, which can be released in nuclear reactions.

COULOMB'S LAW

How particles interact with each other is governed by a physical relationship called Coulomb's Law:

F = k Q1 Q2 / d^2

Or, the force (of attraction or repulsion) is given by a physical constant times the product of the charges, divided by their distance of separation squared.  The proportionality constant (k) is used to make the units work out to measurable amounts.

Note that this is an inverse square relationship, just like gravity.

The "big 3" particles you've heard of are:

proton
neutron
electron

However, only 1 of these (the electron) is "fundamental".  The others are made of fundamental particles called "quarks""

proton = 2 "up quarks" + 1 "down quark"
neutron = 2 "down quarks" + 1 "up quark"

There are actually 6 types of quarks:  up, down, charm, strange, top, & bottom.  The names mean nothing.

Many particles exist, but few are fundamental - incapable of being broken up further.

In addition, "force-carrying" particles called "bosons" exist -- photons, gluons, W and Z particles.

The Standard Model of Particles and Interactions:

http://www.pha.jhu.edu/~dfehling/particle.gif

Online chat time moved to Monday night

Folks- I am still out of town at the moment. I will be available tomorrow evening (Monday) at 8 pm if you have questions.  I'll also be on campus around 6 on Tuesday prior to the exam.

Optics questions - answers forthcoming

1.  Review the concept of reflection, particularly the law of reflection.  Draw what happens when a light ray hits a mirror at various angles.

2.  Review the concept of refraction:  what it is, what causes it, what happens during it, under what circumstances does light bend, etc.  Draw what happens when a light ray hits a block of transparent plastic at various angles.  

3.  Show how to calculate the wavelength of WTMD's signal (89.7 MHz).

4.  Some questions related to how light is affected by optics.

Answers:

Exam 2 topics. Exam is in one week. We will NOT have class this Thursday, 4/7/16

 Please note - we will NOT have class this Thursday, 4/7/16.  I must be away for a funeral.

Lens/Mirror practice problems forthcoming.  

This Sunday, from 8-9 PM, I will be online.  Email me at seanplally@gmail.com, if you have test questions.  I'll be able to provide a speedy response then.  Thanks.


Exam 2 topics:


Energy
Basics of flight; Bernoulli effect

waves

- wavelength

- frequency

- speed

-amplitude

- crests and troughs

wave speed = frequency x wavelength

(Note that the wave speed is the speed of light when you are talking about electromagnetic waves.)

mechanical vs. electromagnetic waves

harmonics on a string - "standing waves"

music - octaves, the next note on the piano (1.0594)

Doppler effect

- red shift, blue shift

light reflection

light refraction

lenses and mirrors (convex and concave)

real and virtual images

focal length

predicting light paths

electromagnetic spectrum