Circuit problems - 1

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

2. 10 coulombs of charge flows past a point in a circuit in 5 seconds. What is the current?

3.  What is the resistance of a light bulb that allows 2 A of current through it when connected to a 12-V battery?

4. A 5-ohm resistor is connected to a 10-volt battery. What current passes through the resistor?


These problems are based on material we will cover next class.

5. Two 100-ohm resistors are in series. What is their total resistance?

6.  In general, what is the difference between resistors in series and in parallel?  Recall the light bulb examples.

7.  Which has more resistance, 2 identical bulbs in series or the same 2 identical bulbs in parallel?

8.  For question 7, which set-up (series or parallel) would kill the battery quicker?

9.  You have 2 bulbs in series - remove one (unscrew it) and what happens?

10.  You have 2 bulbs in parallel - remove one (unscrew) and what happens?

11.  Draw the symbols for battery, resistance and wire.

Test correction

Some of you picked up your test tonight (Wednesday) and left early.  A mistake was found in the key.  Please bring your exam on Monday so that I can check to see if you will be given an extra point.

Thanks, and sorry for that.

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?

Introduction to electricity - 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

Interference, Diffraction and Holography

iffraction

Consider 2 waves meeting each other in the same space.  Their energies (amplitudes) can add or subtract.  This phenomenon is called interference.  If you've ever added sine waves on a calculator before, the effect is similar.

Crests can add to other crests, or cancel with troughs.  However, it is usually some combination (depending on the waves in question).  And often, beautiful "interference patterns" can result.

Diffraction is the phenomenon wherein light waves pass through small openings - the openings cause "new" waves to form, and these "new" waves interfere with each other.

Diffraction and Holography

Holography

Holography is a direct application of interference patterns - indeed, it is the recording of an interference pattern on film, reconstructed with a laser.

Holography is an interference phenomenon caused by two beams - a reference beam (coming from a laser), and an object beam (which reflects off the object).  This interference pattern is burned into the film emulsion of the holographic film.  It can be reconstructed when light passes through it again.

Additional test prep questions....

.... focusing (get it?) on the most recent material.

1.  What is the focal point of a concave mirror or convex lens?

2.  What are real and virtual images?  How are they primarily different?

3.  What causes nearsightedness and farsightedness?

4.  Do all lenses and mirrors give real images?

5.  Under what circumstances do (real) images form AT the focal point of a lens or mirror?

6.  Do plane/flat mirrors (like bathroom mirrors) form real images?

7.  What primary factor(s) affect where images form (from lenses and mirrors) and how big they are?

8.  What are red shifts and blue shifts?  Under what circumstances do they occur?

9.  If a police car approaches and then passes you, what do you notice about the frequency of its siren?

10.  All EM waves in a vacuum have the same _____.

11.  Once EM waves pass from a vacuum into a different medium, what exactly happens?

12.  What exactly causes rainbows, or light breaking up from a prism?  Could you get a rainbow from only pure red light passing through a prism?

13.  How is total internal reflection related to fiber optics?

14.  If you were standing on the shore of a pond and aimed a laser into the water (at some angle), what path would the laser beam take?  Draw this.

Test topics

Waves - mechanical and EM

Wave speed equation

Frequency, wavelength and speed

Harmonics

Music - octaves, semi-tones (1.0595)

Flame tube

Chladni plates

Doppler effect

EM spectrum

Light

Reflection

Refraction

Speed of light

Predict wave path

Lenses and mirrors (concave and convex)

Flat/plane mirrors

Total internal reflection

Image formation

Real and virtual images

Eyesight and problems with it

Eye problems.

In nearsightedness (myopia), the eyeball is too long - images would form in front of the retina (if they could), but there is nothing there onto which the image can be projected.  So, the 'out of focus' rays land on the actual retina.  You can use a concave (diverging) lens to "pre" spread out the rays, so that they hit the retina in focus.

Similarly for farsightedness (hyperopia), the eyeball is too short.  Images would form "behind" the retina if they could, but the actual retina gets in the way.  So, you can use a convex (converging) lens to "pre" converge the rays so that they actually hit the retina in focus.

How do mirrors form images?

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.

How do lenses form images?

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, WHEN THE RAYS ARE INITIALLY PARALLEL.  In contrast, virtual images form via concave lenses under ALL circumstances.