Class cancelation

I'm stuck with a trapped car in a parking lot, courtesy of a downed branch and power lines. It's an interesting lesson in high voltage power, but alas, I'm going nowhere until at least 8.

Plus, it looks all different sorts of unsafe on the roads, for you commuters.

Circuit problems.

1. Distinguish between V, I, R and P.  (P is power - we did not yet chat about that, but it's in the notes.)

2. Give the units for each above.

3. What's Ohm's law?

4. If a 9-V battery is connected to a 2-ohm resistor, how much current flows through the resistor?

5. What's the difference between series and parallel circuits?

6. What exactly is a circuit?

7. Consider identical bulbs in series - how does the brightness change (if at all) as more bulbs are added in series?

8. Answer this question for bulbs in parallel.

9. 2 bulbs in series vs. 2 bulbs in parallel - how do the brightnesses compare?

10. Draw the schematic symbols for battery, wire and resistor.

11. What has more resistance: 2 resistors in series or the same 2 resistors in parallel?

12. Determine a suitable analogy for V, I, and R.

13. Bulbs in series vs bulbs in parallel: if one is unscrewed in either case, what happens to the other bulbs (do they get brighter, go out, or is there no change)?

Circuit and charge problems

1. Distinguish between a proton and electron - how are they similar/different?

2.  How is the coulomb of charge related to the actual charge of a proton or electron?  How does it compare?

3.  Draw the schematic for a simple light bulb and battery circuit.  Identify what the symbols represent.

4.  Describe the difference between voltage, current and resistance.  Give the proper units, too.

5. 10 coulombs of charge flows past a point in a circuit in 5 seconds. What is the current?

6. A 10-volt battery is connected to a resistor.  If 2 amps of current pass through the resistor, what is the resistance of this resistor?


Several students have asked about forming a study group.  Please email me that you are interested and I'll create a list for sharing - you can all work out the details of when/if you meet:

seanplally@gmail.com


Good weekend!

Circuits - 2 / Series and Parallel

Voltage (V) - amount of available energy per coulomb of charge.  The unit is volt (also V).

Current (I) - how quickly charge travels (or charge per time, q/t).  The unit (a coulomb per second) is called the ampere (or amp, A). 

Resistance (R) - a way of expressing how much charge is resisted through a device.  It is expressed as a ratio of applied voltage to the resulting current (V/I).  The unit (a volt per amp) is called an ohm (represented as the Greek symbol omega).

Often, the relationship between V, I and R is expressed as Ohm's Law:

V = I R

Batteries and other sources (such as wall sockets) "provide" voltage, which is really a difference between TWO points (marked + and - on a battery).  A wall outlet is a bit more complex - there are 2 prongs, but often also a third prong (the "ground", for safety purposes).

Some folks like analogies.  Consider the water analogy discussed in class.  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.

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 full path to take.

But there is an exception:

If the supplied voltage is high enough, charge can "jump" an "open circuit." This is clearly a dangerous situation, and one way in which a person can get shocked. Think of the unfortunate situation of sticking your finger (or a paper clip, etc.) into an electrical outlet (or something like a toaster, for that matter). You would "bridge" the circuit, becoming in effect, a resistor.

That's bad.

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. 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 images below, the first 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.

Circuits - 1

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).  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).

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

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

But 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 full path to take.

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

Summary:

Voltage (V) - amount of available energy per coulomb of charge.  The unit is volt (also V).

Current (I) - how quickly charge travels (or charge per time, q/t).  The unit (a coulomb per second) is called the ampere (or amp, A). 

Resistance (R) - a way of expressing how much charge is resisted through a device.  It is expressed as a ratio of applied voltage to the resulting current (V/I).  The unit (a volt per amp) is called an ohm (represented as the Greek symbol omega).

Power (P) - rate at which energy is produced or expended (E/t).  Energy per time.  Unit is the joule per second, called a watt (W).  In electricity:  P = I^2 R

Batteries and other sources (such as wall sockets) "provide" voltage, which is really a difference between TWO points (marked + and - on a battery).  A wall outlet is a bit more complex - there are 2 prongs, but often also a third prong (the "ground", for safety purposes, through which excess charge can travel back to the Earth).

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.  Explain the demonstrations from class, particularly the rotating meter stick.

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

4.  What does atomic number mean?

5.  What is the most common element, and why?

6.  What are quarks?

Standard Model FYI

http://en.wikipedia.org/wiki/Standard_Model

http://www.particleadventure.org/

http://holofractal.net/wp-content/uploads/2013/05/particle.gif

See the last image for a hi-res chart.  Click on it to make it easier to read.

Introduction to Electricity

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.

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

In different words:

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.

Eye trouble

Mirrors

Recall that light reflects from mirrors, according to the law of reflection.  However, it the mirrors is curved, light still obeys this rule - it just looks a bit different.  You have to visualize the curved mirror as a series of little flat mirrors.

A convex mirror (top) acts just like a concave lens - only virtual images are formed.  Think of convenience store mirrors.

 A concave mirror (bottom) acts just like a convex lens.  Think of makeup/shaving mirrors.

Lenses

Lenses

As shown and discussed in class, light refracts TOWARD a normal line (dotted line, perpendicular to surface of lens) when entering a more dense medium.

Note, however, that this direction of bend changes from down (with the top ray) to up with the bottom ray. This is due to the geometry of the lens. Look at the picture to make sure that this makes sense.


The FOCAL LENGTH (f) of a lens (or curved mirror) where the light rays would intersect, but ONLY IF THEY WERE INITIALLY PARALLEL to each other. Otherwise, they intersect at some other point, or maybe not at all!

FYI:  The location of images can be predicted by a powerful equation:

1/f = 1/di + 1/do

In this equation, f is the theoretical focal length (determined by the geometry of the lens or mirror), do is the distance between the object and lens (or mirror) and di is the distance from lens (or mirror) to the formed image.

We find several things to be true when experimenting with lenses. If the object distance (do) is:

greater than 2f -- the image is smaller
equal to 2f -- the image is the same size as the object (and is located at a di equal to 2f)
between f and 2f -- the images is larger
at f -- there is NO image
within f -- the image is VIRTUAL (meaning that it can not be projected onto a screen) and it appears to be within the lens (or mirror) itself

If an image CAN be projected onto a screen, the image is REAL. Convex lenses (fatter in the middle) and concave mirrors (like the inside of a spoon) CAN create real images - the only cases where there are no images for convex lenses or concave mirrors are when do = f, or when do < f. In the first case, there is NO image at all. In the second case, there is a magnified upright virtual image within the lens.

Concave lenses (thinner in the middle) NEVER create real images and ONLY/ALWAYS create virtual images. This is also true for convex mirrors (like the outside of a spoon, or a convenience store mirror).

Play around with this applet:

http://www.physics.metu.edu.tr/~bucurgat/ntnujava/Lens/lens_e.html

Convex lenses (which are defined to have a positive focal length) are similar to concave mirrors.

Concave lenses (which are defined to have a negative focal length) are similar to convex mirrors.


This is a bit more complicated, but here are some images and information for mirrors:

http://www.physicstutorials.org/home/optics/reflection-of-light/curved-mirrors/concave-mirrors


>

http://www.physics.metu.edu.tr/~bucurgat/ntnujava/Lens/lens_e.html

The key thing to note is that whether or not an image forms, and what characteristics that image has, depends on:

- type of lens or mirror
- how far from the lens or mirror the object is

In general, convex lenses and concave mirrors CAN form "real" images.  In fact, they always form real images (images that can be projected onto screens) if the object is further away from the lens/mirror than the focal length.

If the object is AT the focal point, NO image will form.

If the object is WITHIN the focal point, only virtual images (larger ones) will form "inside" the mirror or lens.

Concave lenses and convex mirrors ONLY form virtual images; they NEVER form real images.  Think of convenience store mirrors and glasses for people who are nearsighted.

http://www.physics.metu.edu.tr/~bucurgat/ntnujava/Lens/lens_e.html

But when the light rays are initially PARALLEL, convex and concave lenses act as follows:

A real image forms at the focal length of a convex lens, and only virtual images form via concave lenses.

Optics hw

2.  Review the concept of refraction:  what it is, what causes it, what happens during it, under what circumstances does light bend, etc.

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

4.  What are the differences between mechanical and electromagnetic waves; give examples of each.

Test 2 topics, more or less

center of mass (and torque)

energy

waves

- wavelength

- frequency

- speed

-amplitude

- crests and troughs

speed = frequency x wavelength

(same equation as above, but with c for speed, when waves are electromagnetic)

mechanical vs. electromagnetic waves

harmonics

music - octaves, 1.0594

Doppler effect

- red shift, blue shift

sound in (organ) pipes

light reflection

light refraction

index of refraction

lenses and mirrors (convex and concave)
electromagnetic spectrum

Light - 2 ---- Refraction

Reflection - light "bouncing" off a reflective surface. This obeys a simple law, the law of reflection!

The incident (incoming) angle equals the reflected angle. Angles are generally measured with respect to a "normal" line (line perpendicular to the surface).

Note that this works for curved mirrors as well, though we must think of a the surface as a series of flat surfaces - in this way, we can see that the light can reflect in a different direction, depending on where it hits the surface of the curved mirror. More to come here.

Refraction:

Refraction is much different. In refraction, light enters a NEW medium. In the new medium, the speed changes. We define the extent to which this new medium changes the speed by a simple ratio, the index of refraction:

n = c/v

In this equation, n is the index of refraction (a number always 1 or greater), c is the speed of light (in a vacuum) and v is the speed of light in the new medium.

The index of refraction for some familiar substances:

vacuum, defined as 1

air, approximately 1

water, 1.33

glass, 1.5

polycarbonate ("high index" lenses), 1.67

diamond, 2.2

The index of refraction is a way of expressing how optically dense a medium is. The actual index of refraction (other than in a vacuum) depends on the incoming wavelength. Different wavelengths have slightly different speeds in (non-vacuum) mediums. For example, red slows down by a certain amount, but violet slows down by a slightly lower amount - meaning that red light goes through a material (glass, for example) a bit faster than violet light. Red light exits first.

In addition, different wavelengths of light are "bent" by slightly different amounts. This is trickier to see. We will explore it soon.

Refraction, in gross gory detail

Consider a wave hitting a new medium - one in which is travels more slowly. This would be like light going from air into water. The light has a certain frequency (which is unchangeable, since its set by whatever atomic process causes it to be emitted). The wavelength has a certain amount set by the equation, c = f l, where l is the wavelength (Greek symbol, lambda).

When the wave enters the new medium it is slowed - the speed becomes lower, but the frequency is fixed. Therefore, the wavelength becomes smaller (in a more dense medium).

Note also that the wave becomes "bent." Look at the image above: in order for the wave front to stay together, part of the wave front is slowed before the remaining part of it hits the surface. This necessarily results in a bend.

The general rule - if a wave is going from a lower density medium to one of higher density, the wave is refracted TOWARD the normal (perpendicular to surface) line. See picture above.

http://stwww.weizmann.ac.il/lasers/laserweb/java/twoangles2.htm

http://lectureonline.cl.msu.edu/~mmp/kap25/Snell/app.htm

http://www.physics.uoguelph.ca/applets/Intro_physics/refraction/LightRefract.html

LIGHT - 1

Recall that waves can be categorized into two major divisions:

Mechanical waves, which require a medium. These include sound, water and waves on a (guitar, etc.) string

Electromagnetic waves, which travel best where there is NO medium (vacuum), though they can typically travel through a medium as well. All electromagnetic waves can be represented on a chart, usually going from low frequency (radio waves) to high frequency (gamma rays). This translates to: long wavelength to short wavelength.

All of these EM waves travel at the same speed in a vacuum: the speed of light (c). Thus, the standard wave velocity equation becomes:

c = f l

where c is the speed of light (3 x 10^8 m/s), f is frequency (in Hz) and l (which is the Greek letter, lambda) is wavelength (in m).

General breakdown of e/m waves from low frequency (and long wavelength) to high frequency (and short wavelength):

Radio

Microwave

IR (infrared)

Visible (ROYGBV)

UV (ultraviolet)

X-rays

Gamma rays

In detail, particularly the last image:

http://hyperphysics.phy-astr.gsu.edu/hbase/ems1.html

http://csep10.phys.utk.edu/astr162/lect/light/spectrum.html

http://www.unihedron.com/projects/spectrum/downloads/full_spectrum.jpg

Don't forget - electromagnetic waves should be distinguished from mechanical waves (sound, water, earthquakes, strings on a guitar/piano/etc.). 

ALL E/M waves (in a vacuum) travel at the SPEED OF LIGHT (c).

The Doppler Effect

http://www.lon-capa.org/~mmp/applist/doppler/d.htm

http://falstad.com/mathphysics.html

Run the Ripple tank applet -

http://falstad.com/ripple/

The key in the Doppler effect is that motion makes the "detected" or "perceived" frequencies higher or lower.

If the source is moving toward you, you detect/measure a higher frequency - this is called a BLUE SHIFT.

If the source is moving away from you, you detect/measure a lower frequency - this is called a RED SHIFT. Distant galaxies in the universe are moving away from us, as determined by their red shifts. This indicates that the universe is indeed expanding (first shown by E. Hubble). The 2011 Nobel Prize in Physics went to local physicist Adam Riess (and 2 others) for the discovery of the accelerating expansion of the universe. Awesome stuff!

http://www.nobelprize.org/nobel_prizes/physics/laureates/2011/

It's worth noting that the effect also works in reverse. If you (the detector) move toward a sound-emitter, you'll detect a higher frequency. If you move away from a detector move away from a sound-emitter, you'll detect a lower frequency.

Mind you, these Doppler effects only happen WHILE there is relative motion between source and detector (you).

And they also work for light. In fact, the terms red shift and blue shift refer mainly to light (or other electromagnetic) phenomena.

>

More music-related sites, FYI:

http://www.youtube.com/watch?v=XKRj-T4l-e8

http://www.youtube.com/watch?v=cPALfz-6pnQ

https://www.youtube.com/watch?v=aWAjLOwOHU0

http://www.acs.psu.edu/drussell/Demos/TuningFork/fork-modes.html