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