Download POTD

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…


Or… at 2 meters:



Is equal to 9.81 m/s2 x 2 m x the mass
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


This is the Electric Potential


In units of Joules per Coulomb
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?
E1 – field
strength due to
q1 at “d”
q1
-
Distance
“d”
PE = E1 x q2 x d
PE = k q1 q2 / d
+
q2
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

Voltage = Current x resistance

V = iR
volts = amps x ohms
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


But the electrons take much longer to move



We see the effect at close to the speed of light
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


Generators


Convert chemical energy into electrical
energy
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

1.
4.
5.
695
400 s
20 C
A) 2.6 mA
b) 1.6 x 1017 ec) 5.1 mA

1.
2.
3.
4.
5.
6.
703
0.43 A
1.8 A
A) 2.5 A b) 6 A
110 V
46 ohms
A) 0.41 A
b) 0.59 A
Resistance

Resistance is…well


Resistance increases when




Resistance to the flow of charge
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 = qV
So…


=ΔPE / Δt
P = Vq/Δt
P=Vi
Light bulb goes on…

A 60 watt light bulb is turned on…



P = Vi



The voltage of the system is 120 V
What is the current?
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:



Defined relationship between voltage,
current, and resistance.
Dismissed by his colleagues.



Bavaria in 1787
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



Total voltage of a series system



One at a time
Until it reaches the other side of the voltage source
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



The resistors have to share “voltage drop”



Doesn’t get used up…
Must have same value through entire circuit
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





5Ω
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

1.
2.
3.
4.
710
14 Ω
58,000 Ω
22 Ω
6.25 A; 312 W

2.
3.
4.
739
24 Ω; 1.00 A; 1.00
A
1.0 V; 2.0 V; 2.5 V;
3.5 V
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…


Wanted to add another wheel for oats


Like 2 loads on one water wheel
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 = i 1 + 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 + …


v/R = v1/R1 + v2/R2 + v3/R3 …


Substituting I = v/R
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.
3.
4.
50 Ω
A) Req = 2.2 Ω
B) 6 A, 3 A, 2 A
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.
WWWT