Electricity! February 22/23, 2010. Electrical Potential Energy Remember gravity? And gravitational...

Electricity!

February 22/23, 2010

Electrical Potential Energy

Remember gravity? And gravitational potential energy? “PE = mgh”

The higher you go the more PE you have… Consider the ladder at 2 meters high.

What’s the PE of an object with a mass of 5 kg? How about 10 kg?

Electrical PE

Electrical energy is very similar If we take a “+” charge and pull it away from

a “-” charge We do “work” on it (force x distance)

We create potential energy

If you let it go Smaaackkk… It flies towards the “-” charge Making kinetic energy

Let’s go back to the ladder

Potential due to gravity at 2 meters… Is equal to 9.81 m/s2 x 2 m x the mass

Or… at 2 meters: The PE = 19.6 m2/s2 x whatever mass you have

The gravitational “potential” is equal to 19.6 J per 1 kg of mass

No matter what you take up the ladder The PE is 19.6 J/kg x the mass (kg)

Electrostatics –big copy cat

If you look at the potential energy per unit charge… PE/# charges

In units of Joules per Coulomb

This is the Electric Potential NOT Potential ENERGY

For every Coulomb of charge at some location You get so many Joules of potential energy

What’s it called?

Named after a strange Italian Whose name was Antonio…

Volta!

Note that a Volt Doesn’t tell us how much energy is

present Just how much energy per unit of charge

Volts don’t kill

Consider a raindrop a mile up in the air It has a lot of “gravitational potential” This is like voltage

But not much mass Mass is like the charge

Which would you prefer?

To be hit by a rain drop that started falling 1 mile up

Or… Hit by piano that started falling 10 feet

up? What is the connection to electricity?

Potential Energy – electrically speaking…

PE = E x q x d This is like Force x distance Which is “work”

Work done on an object gives it PE

PE = E x q x d = (kq1/d2) x q2 x d

= kq1q2/d

What does this look like?

- +Distance “d”

E1 – field strength due to q1 at “d”q1

q2

PE = E1 x q2 x d

PE = k q1 q2 / d

Electric PE

The electric potential energy between 2 charged objects is 0.10 J

Each object has a charge of 4.0 x 10–6 C How far apart are they? PE = kq1q2/d

d = kq1q2/PE d = 9x109Nm2/C2 x 4x10-6C x 4x10-6C/0.1 J

d = 1.44 m

Let’s clarify…

PEelec – electric potential energy Volt is the potential energy per unit

charge AKA “Electric potential”

ΔV = “Potential difference”

No difference in PE - so no flow of water (charge).

Increase “gh” of one end…like voltage difference

Now for something more concrete…

No longer static

Elements of electricity Voltage difference (V) Current (I) Resistance (R)

Voltage we’ve already started to explore…

But we just got started!

Now… let’s measure some volts!

The Electric Light Bulb

Electricity – closer to Ohm

February 18/19, 2009

Circuits “unplugged”

Homework

2) 4.5 meters 4) 1.60 x 10 –19 C

2) position, charge, electric field strength

4) No, but usually choose reference point that sets initial PE = 0

Remember?

Think, don’t speak… What were the 3 parts of an electric

circuit… Tell a neighbor or write it down Can you describe voltage?

Current

Charge per time Like a “charge” flow rate

Units of ampere “amp”Coulomb/second = 1 amp

C/s

Current calculation

The current in a light bulb is 0.835 A. How long does it take for a total charge of 1.67 C to pass a point in the wire?

ΔQ = 1.67 C I = 0.835 A Δt = ΔQ/I = 1.67(C) / 0.835(C/s) = 2.00

s

Resistance

This is why we want electricity…

Measure in ohms (Ω)

Ohm’s Law

V = iR

volts = amps x ohms

Voltage = Current x resistance

sooooo

Voltage is proportional to Current and resistance

How are…Current and resistance related?

12 volt battery

30 ohms of resistance What is the current? V = iR 12 V = i (30Ω) i = 0.4 A

Let’s assume…

Using the hand generators… And you generate 0.25 amps of current

Resistor was 5.0 Ω What is the current?

Drawing circuits…

Current topics

Moving charge must be 1 of 3 varieties: Positive Negative Both

Current is “defined” as flow of positive charges

Against the tide…

So if a positive charge is moving forward…

That is like a negative charge moving backwards…

What is actually moving?

When you set current in motion You really just cause electrons to bump

into one another They pass along the energy without

moving all the way Like dominos

Drift Velocity

Turn on the light switch We see the effect at close to the speed of light

But the electrons take much longer to move There is some random movement With an overall motion in the direction of the

electric field This overall motion is called the Drift Velocity

About 1 meter per hour

Sources of current

Batteries Convert chemical energy into electrical

energy Generators

Convert mechanical energy into electrical energy

Electric energy is converted into some useable form at the “load”

AC DC

Alternating current Sine wave current (washing machine) Constantly changes sign – vibrates back

and forth. Direct current

Steady current at a particular voltage

Measuring voltage

Always measure “across” a resistance or voltage drop

The volt meter gets hooked up “in parallel”

Hugs

Measuring current

Always measure current “in line” The ammeter gets hooked up in

series. “Holds hands”

Ohm’s Mill

February 20/23, 2009

Homework

695

1. 400 s

4. 20 C

5. A) 2.6 mAb) 1.6 x 1017 e-

c) 5.1 mA

703

1. 0.43 A

2. 1.8 A

3. A) 2.5 A b) 6 A

4. 110 V

5. 46 ohms

6. A) 0.41 A

b) 0.59 A

Resistance

Resistance is…well Resistance to the flow of charge

Resistance increases when The length of the carrier increases The diameter of the carrier decreases The temperature increases

It also varies with material

PE, Work & Power

Let’s look at a simple circuit And think about the energy transfers

PE gained across the battery… Is lost across the resistor “Voltage drop”

How much Power?

Power = work divided by time P = W/Δt

=ΔPE / Δt ΔPE = qV So…

P = Vq/Δt P = V i

Light bulb goes on…

A 60 watt light bulb is turned on… The voltage of the system is 120 V What is the current?

P = Vi I = P/V I = 60 W/120 V = 0.50 A

How much resistance is in a 120W bulb?

There’s more to power…

P = Vi V = iR What is Power in terms of i and R? P = i2R In terms of V and R? P = V2/R

Aha! A 75-watt light bulb!

V = 120 V Determine i and R

I = 0.625 A 75 W = (0.625 A)2 R R = 192 Ω

Higher watts means…

Typically have a constant voltage… More or less current? Less or more resistance?

Now, on to Ohm….

Or… “the disgraced high school teacher”

Life and times

Georg Simon Ohm: Bavaria in 1787

Defined relationship between voltage, current, and resistance.

Dismissed by his colleagues. Ohm resigns from his high-school teaching

position Lived in poverty and shame.

And now…the inside story:

Ohm was a clever lad

Had a small grain mill

Powered by a waterwheel

Ohm pondered the relationship of electricity in his Volta Battery

Then one day…

The series connection

A series circuit is like holding hands Electricity passes through each person

One at a time Until it reaches the other side of the voltage source

Total voltage of a series system V = iReq

Req – resistance that the battery “sees”

Req = R1 + R2 + R3 … For however many there are

What’s that mean?

Current only has one path Doesn’t get used up… Must have same value through entire circuit

The resistors have to share “voltage drop” Energy used is proportional to resistance Total voltage drop = ΣV for all resistors

The power will vary, too Follows voltage

Let’s look at one:

100 volt system 4 resistors

5 Ω 10 Ω 15 Ω 20 Ω

What is the total resistance? Req = ???

Now about that power bill…

What is the voltage drop across each resistor?

What is the current flow? What is the power for the entire

system? How about for each resistor?

Your turn…

A 6 volt battery is hooked up to a 6Ω and 18 Ω resistor in series. What is the Req

What is the current in the system? What is the voltage drop across each

resistor?

Lab

To the table!

Electricity – Parallel Circuits

February 24/25, 2009

Ohm work

710

1. 14 Ω

2. 58,000 Ω

3. 22 Ω

4. 6.25 A; 312 W

739

2. 24 Ω; 1.00 A; 1.00 A

3. 1.0 V; 2.0 V; 2.5 V; 3.5 V

4. a) 11.28 Ω; 0.80 A b) 5.79 V; 3.2 V

5. 0.5 Ω

Series review

If you add a resistor to the circuit What happens to the current?

What happens to the total voltage? What happens to the individual

voltages? Total resistance? Power?

Meanwhile back at the grain mill…

Ohm figured out the series circuit… Like 2 loads on one water wheel

Wanted to add another wheel for oats But it wouldn’t fit…

Parallel circuits didn’t seem to follow the rules… Or did they???

Parallel circuits

Water/current has multiple paths to follow

It seeks the path of least resistance More flow where resistance is less

More flow overall Total current is the sum of all individual

currents i = i1 + i2 + i3 + …

The parallel connection

Voltage is the same for each water pipe in parallel V total = V1 = V2 = V3 = … Each resistor sees the same potential

difference [potential energy] What happens when one path is

stopped?

You may see this in the lab…

i = i1 + i2 + i3 + … Substituting I = v/R

v/R = v1/R1 + v2/R2 + v3/R3 … And since v is constant

1/Req = 1/R1 + 1/R2 + 1/R3 …

Example

12 volt difference 2 resistors in parallel:

R1 = 2 Ω R2 = 4 Ω

Req = ? i = ? (in each section and total) What happens when I add another

resistor in parallel? (R = 6 Ω)

What happens when we add a resistor to the parallel circuit:

To voltage? To current? To Req? To power?

Lab

Demo parallel circuit set up. Where do the ammeters go?

Voltmeters

Voltmeters – in parallel Does it have a big resistor or a small

resistor?

Complex Circuits - intro

What happens when we have a little of both?

Electricity – Complex Circuits

February 26/27, 2009

Homework

2. 50 Ω

3. A) Req = 2.2 Ω

B) 6 A, 3 A, 2 A

4. A) Req = 3.0 Ω

B) 36 V

C) 2 A; 4 A; 6 A

Voltmeters

Voltmeters – in parallel Don’t want it to affect the circuit…

Increase current or affect voltage Does it have a big resistor or a small

resistor?

Ammeter

In series… Again – don’t want it to affect the

circuit… Big resistor or small?

Complex Circuits - intro

What happens when we have a little of both?

Electricity – Review notes

March 6/9, 2009

Short circuit?

What is a short circuit? How does it differ from a break in a

circuit?

What happens…

To resistance if you add a resistor in series? In parallel?

To current if you add a resistor in series? In parallel?

More

The equivalent resistance of two identical resistors in parallel is…

If you start with the situation above and increase the resistance through one of them…the total goes:

What is the maximum resistance of 2 resistors in parallel?

You’ve got the …

Power! P = Vi = i2R = V2/R If the current goes up…

The power???

If, then…

You break a series circuit… You break a parallel circuit… In a complex circuit…

What is wrong with these…

Meters, currents, etc.

WWWTWhat (if anything) is wrong with this picture?