Dec. 19 – Circuits

Last time we talked about Ohm's Law, V = I R.  Which one of these graphs best represents Ohm's Law?

The answer is (a).  If you graph voltage vs. current, and you get a linear graph, that means Ohm's law is obeyed.

Ohmic - the material obeys Ohm’s Law (V vs I graph is linear).

Non-Ohmic - the material does not obey Ohm’s Law (V vs. I graph is curved).

We will always assume Ohmic resistors.

Circuits

Circuits are closed paths for charges to flow.

An analogy of circuits as a roller coaster ride.

Here's what circuits look like in real life.  Every line on the board is a wire.

Conventional current flows from + to –.  Electron flow is opposite ( – to + ).

AC - Alternating Current, direction constantly changes, no + or –.

DC - Direct current, charges only move in one direction.

In this course, we will only be working with DC circuits.

Types of Circuits

Series

 - components are connected with one path

 - total resistance is the SUM of each resistance.

• The current is the same for all resistors connected in series.

Parallel

 - components are connected with multiple paths for charges to flow.

 - total resistance is the INVERSE SUM 

• The voltage is the same for all resistors connected in parallel.

Using these rules, we can replace a set of resistors with an equivalent resistor

 Mixed Circuits

 - contains combinations of components in series or parallel

 - total resistance must be calculated one section at a time

Kirchhoff's Laws

Kirchhoff's Current Law

Also known as the junction rule.

 - All current entering a location must exit that location.

 - Current in equals Current out.

            I in   =  I out

Kirchhoff’s Voltage Law

Also known as the loop rule.

 - The potential difference around a loop must be zero.

           V1 + V2 + V3 + … = 0 

Handout

Here are some challenging circuit questions that are more difficult than the ones in your text book.

• Complex Circuits Practice

Dec. 18 – Speaker Project

Today we assigned the ISP!  You and your group will have to build a speaker!

Handout

• Speaker Project Marking Scheme

Here's a video to help you get started.  You do not need to follow this video!  Use whatever resources you want and whatever design works for you and the materials you have.

Dec. 17 – Unit 5: Electricity and Magnetism

Schedule for the next few classes...

• Today: New Unit
• Tomorrow: ISP assigned, work period, bring laptops/tablets.
• Friday: Lab Due.
• Jan. 5: Welcome back.
• Jan. 6: Quiz on Circuits

Unit 5: Electricity and Magnetism

What is charge?

  - can be positive, negative, or neutral.

  - a source of electric field (force) and also reacts to that force. (ie. charges exert forces on each other).

  - the smallest charge is 1 electron (or proton) = 1.602 x 10 ^-19 C

  - C is Coulombs, units of charge.

  - Unlike gravity, charges attract or repel.

Electric Potential

Electric forces can do work.  Therefore, there is a form of electric energy.  We call it electric potential energy.

The electric potential energy per Coulomb is called “voltage”.  Also called electric potential, or potential difference.

V = ∆E/q

Units are "volts", 1 V = 1 J / 1 C

Like gravitational potential, zero can be at any point, only differences matter.  Often written as ∆V.

Current

The movement of charges.

I = Q/∆t

Units are "amperes", 1 A = 1 C / 1 s

Ohm’s Law

Potential difference makes charge flow, but the flow is restricted by resistance.

Example: 

A flashlight requires 4 AA batteries (1.5 V each).  If the bulb has 500 Ω of resistance, what current goes through the bulb?

     I = V ÷ R  = (1.5 A x 4) ÷ 500 Ω = 0.012 A = 12 mA

b) If the same bulb is plugged into a wall socket (120 V), what current is drawn?

     I = V ÷ R  = 120 V ÷ 500 Ω = 0.24 A = 240 mA

Most houses have 15 A “breakers” for safety.

Example:

A TASER can deliver up to 50 000 V through the air.  Once it contacts you, the voltage drops to 1200 V.  A wall socket provides 120 V.  Which is more dangerous?

The resistance of a human depends on the point of entry, moisture, tissue, etc.

Dry skin, R = 100 000 Ω

Broken skin, R = 1000 Ω

Use broken skin and a wall socket.

I = V/R              I = 120 mA

Taser.

I = V/R             I = 1.2 A

Looks like a Taser is more dangerous… why doesn’t it kill you?  Remember, current is charge/second, if you have limited charge, you have limited current.

A taser has limited charge in the battery.

Taser claims to deliver 0.002 A up to 0.03 A.

Wall socket has unlimited supply of charge.

Handout

• Unit Outline

Dec. 15 – Review and Study Period

Hi Everyone,

I hope your studying for your test is going well.  Many people have asked me for extra questions, so here are a few to tie you over until the test tomorrow:

• Standing Wave Problems

Make sure to get some rest before the test as well.

Good luck!

Dec. 12 – Thinking Question

Here's the thinking question from last year:

• Thinking Question
• Thinking Question Solutions

Good luck in your studying!

Dec. 11 – Lab

Today we did the lab!  Remember, the lab is due on Dec. 19.

Here are some additional materials you might find useful, solutions to former worksheets.

• Superposition Exercises Solutions
• Formative Quiz Solutions

Tomorrow we will do the previous thinking question and a work period.

Dec. 10 – Doppler Shift, Lab and Quiz

Today we played with an Airzooka!

Then we finished up the Doppler shift and discussed the next few days.

Here are the notes:

Handouts

• Speed of Sound Lab
• Formative Quiz

You should now be able to do all the textbook homework from the Unit Outline.

Reminder: the unit test is next Tuesday!

Dec. 9 – Sound intensity level, Beats and Doppler Effect

Many topics to cover today and not a lot of time, so here are the notes:

I didn't have time to finish the derivation in class, so we will continue it tomorrow.  For now, enjoy this video about sonic booms.

Homework

You can now complete the homework on the characteristics of sound from the unit outline.

Test Solutions

Here are the solutions to the test I handed back today:

• Test Solutions Period 2
• Test Solutions Period 5

Dec. 8 – Resonance and Characteristics of Sound

Handout

• Frequency of standing waves 

Last week we discussed how wavelength of a standing wave is related to the length of the spring.  This handout explains how the same length is related to frequency.  The important thing to take away is that all harmonics have frequencies that are related to the fundamental frequency by simple multiples:

f1 = v/(2L)
f2 = 2 x f1
f3 = 3 x f1
f4 = 4 x f1

Resonance

Every system has a fundamental frequency, f1, that supports a standing wave.

f1, depends on the physical features of the system (length, density, temperature, etc).

Driving Force: A force that causes the oscillations.

When a driving force matches the fundamental frequency, the system will resonate.  The amplitude of the oscillation will increase to the limit of the system.

Example: The Tacoma Narrows Bridge.

Example: Earthquakes and buildings.

I also showed many other examples using my bowl, a spring, a metal bar, and the example of a kid on a swing.

More on Sound

 - Longitudinal wave in air, composed of compressions and rarefactions.

 - Wavelength is the distance between two compressions.

 - Frequency is directly related to pitch.

 - Amplitude is directly related to volume.

Humans can hear between 20 Hz and 20 000 Hz.

The speed of sound depends only on the medium (not on frequency or intensity).  You can only change the speed of sound by changing the air. ie. temperature.

In this equation, the speed of sound is in m/s and T is in degrees Celsius.

The speed of sound is referred to as Mach 1.

• Mach 2 is twice the speed of sound.
• Mach 3 is three times the speed of sound.
• etc...

Intensity

The intensity of sound (volume) is measured in Watts per meter squared.

  W / m^2

If area increases, intensity decreases.

Intensity is not often used because we can hear an incredibly large range of sound from  10^-12 W/m^2 up to 10 W/m^2.  That's a difference from 0.000000000001 W/m^2 up to 10 W/m^2!

We use a different scale to measure sound intensity called decibels.

Sound Intensity Level (dB)

More on this tomorrow....

Homework

Try the questions on the back of today's handout.

Dec. 6 – Standing Waves

Today we discussed standing waves and I showed you how to set up transverse and longitudinal standing waves on springs.  We also discussed standing waves in pipes.

Here are the notes:

It's not possible to see standing waves in pipes, but there are clever ways to visualize it using what's called a Ruben's tube:

Here's one playing some music that you might know:

Here's what two dimensional standing waves look like:

... and a two dimensional Ruben's tube!

Dec. 4 – Superposition of Waves

Some quick notes with some activities today.  Here are the notes:

Superposition of waves

Interference: when two pulses or waves appear at the same place in a medium.

What happens to the two pulses or waves?

When the two pulses interfere, their amplitudes add up.

Superposition principle: When two waves interfere, the resultant amplitude is the sum of the two individual amplitudes.

Constructive interference: when two waves interfere to create a larger amplitude.  This happens when the waves are “in phase”.

Constructive interference (in phase).

Destructive interference: when two waves interfere to create a smaller amplitude.  This happens when the waves are exactly "out of phase".

Destructive interference (out of phase).

Alternatively constructive and destructive interference.

Handouts

• Superposition Activity
• Superposition Excercises

Dec. 3 – Properties of Waves

Today we played with some more toys that demonstrated waves, including this thing:

This device is called a Bell wave machine an is used to demonstrates how waves work.

Wave Reflection

What happens when a wave hits the end of the medium?  We did it with the Bell wave machine pictured above and with this online simulation:

• http://phet.colorado.edu/en/simulation/wave-on-a-string

We can summarize the results as follows:

• When a wave hits the end of the medium, it is reflected.
• If the boundary is rigid (fixed) the reflected wave is inverted.
• If the boundary is loose the reflected wave is upright (on the same side of the equilibrium).

More Definition

-  Oscillation: a motion that repeats itself

-  Cycle: the point where an oscillation begins to where it repeats (same as one wavelength)

-  Period: the time it takes to complete one cycle, T (measured in seconds)

     The period of a wave is related to its frequency.

     T = 1 / f        or     f = 1 / T

Speed of a Wave

From kinematics v = ∆d / ∆t

For a wave, ∆d can be the wavelength (lambda).  ∆t can be one period.

Therefore:   v = 入 / T

or in terms of frequency

                  v = 入 f

This is called the Universal Wave Equation!

- works for ANY wave in any medium

Handout

• Universal Wave Equation Worksheet

More demonstrations

We also played with this tone generator to see if we can all hear the same sounds.

• Online Tone Generator

It turned out I couldn't hear any sounds with a frequency over 15 000 Hz, but you guys can!

Dec. 2 – New Unit: Waves and Sound

Congratulations on finishing the Energy Unit!

I'm testing out a new app from google that will allow me to collect forms and information.  I would really appreciate it if you try it out.  If it works, we can do formative quizzes and other neat stuff in the future.  Please click on the link and try out this new tool:

• http://goo.gl/forms/Vcflxyb49K

Time for a New Unit!

Unit 4: Waves and Sound

• Unit Outline

Most important information...

• Next Test date is Dec. 16

First of all, what is this?

These people are doing a "wave", but what exactly is moving? Their arms go up and down, but what is moving from left to right?  We discussed this today in class using springs and videos:

Here are the notes and definitions from today's class.

Definitions:

Wave - A disturbance or variation that transfers energy from point to point.

Particles of the material are not being transferred, only the energy.

Examples:

 - springs

 - water

 - microwaves

 - sound

Ripples are an example of water waves.

Microwaves are an example of electromagnetic waves.

Mechanical Waves vs. Electromagnetic Waves

 - Mechanical waves have a medium that carries them. e.g. sound is carried by air (air is the medium)

 - Electromagnetic waves do not require a medium.

More Definitions:

 - Wave pulse: a single disturbance

 - Amplitude: The size of the disturbance (always positive)

 - Equilibrium: the state of the medium with no disturbance.

 - Crest: the point of maximum amplitude

 - Trough: the point of maximum negative amplitude.

 - Wavelength: the distance between two crests (or two troughs), “lambda”

 - Frequency: number of pulses per second.

    units are “per second” = Hertz

    1 / second = 1 Hz

Ex: You breath 20 per minute.  What is the frequency of your breath?

20 / min 20 / min ( 1 min / 60 seconds )   <-- write it as a fraction to see how minutes cancel             = 0.333 /s              = 0.333 Hz
You are breathing at 0.333 Hz.

Transverse vs. Longitudinal Waves

Transverse: the disturbance is perpendicular to the direction of the wave.

Longitudinal: the disturbance is parallel to the direction of the wave.

   - compression: the point of maximum density

   - rarefactions: the point of minimum density

   Eg: Sound is a longitudinal wave.

Just for fun...

Here's the difference between AM and FM radio waves: