Download Physics - Unit 10 – Electrical Energy, Current and Power

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AP Physics – Electrical Energy, Current, and Power Introduction – Prerequisite for Circuits
NOTES
Unit Outline:
This unit sets us up for circuits. It introduces the circuit terminology and concepts.
1. EPE electrical PE.
Relate to gravitational PE
Derive the 2 equations
2. V – Voltage (Potential Difference)
EPE per charge
3. C - Capacitance – Storing EPE – storing charge
4. I – Current – the flow of charge (electrons)
How electrons flow and transfer energy
5. R – Resistance – impeding the flow of charge
Factors that affect resistance
Batteries
P – Power
Power companies – calculating power consumption
EPE
What are types of PE?
CPE, Elastic PE, GPE, EPE
We are going to look at Electrical PE. It’s very similar to GPE.
EPE quantifies how a charge will move in an electric field, based on its position in the field.
GPE = m ag h
EPE = -qEd
(for gravity, m causes the force, for electricity, q causes the force)
(for gravity, ag is the strength of the pull of gravity, electricity, E shows the strength of the pull)
(gravity, h is the distance, instead we use d as distance (same thing). – d must be in the direction of the field)
( - sign means it’s based on a + charge, well find out soon the direction electrons flow is +)
This is for a uniform E field. (draw pictures to describe why)
What’s the units for energy???? Joules.
Therefore EPE units are Jouls as well.
Another way to write EPE that is often useful when the field is not uniform. For example between multiple
objects.
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Start with Work
W = Fx
W = EPE = F x
F x = (Kc q1 q2/r2) x
Isn’t x and r the same thing ? distances? Therefore 1 cancels out:
EPE = kc q1q2 / r
So that’s the two versions of EPE, one for a uniform field, and one for a non-uniform field (multiple objects).
Potential Difference V
Often when making circuits, it’s cumbersome to use the EPE equations in order to determine circuit properties.
Instead of dealing with the EPE of a bunch of charges, it’s easier to deal with the EPE per charge. Specifically,
the change in EPE per charge.
We will see later how much more useful this expression is.
The change in EPE per charge is called potential difference. The difference in potential energy. The symbol
for it is “V”, which you know as Voltage.
V = EPE / q
V = (-qEd) / q
- notice 1 q cancels out. Therefore V = - Ed
The unit for Voltage is also a “V”, Volts
Ex: 12 V battery maintains a potential difference of 12.
Another way to express voltage is by substituting in the other equation for EPE:
V = EPE /q => (kc q1q2/r) /q => kc q/r
V = kc q/r
So the V equations are simply the EPE equations with a “q” divided out.
Applications :
One of the best applications of the concept of EPE and V is a battery.
A battery is a device that maintains a potential difference across its terminals (stores energy).
Example: A 12 V battery has a positive terminal that is 12 V higher in potential than the negative terminal.
This difference in potential allows electrons or current to flow when the two terminals are connected.
Practice worksheet with EPE and V
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Capacitance
A battery is a device that maintains a difference in electrical potential energy.
What is a device that stores charge?
A capacitor is a device that stores charge.
Why would you want to store charge??
A charged capacitor acts as a storehouse of charge and energy that can be used at a later time.
Capacitors are used in almost every electronics application, from keys on a keyboard, radio tuners, spark plugs,
flash units, and in general, there are dozens of capacitors in every computer, tv, microwave, cell phone, etc….
Storing charge is relatively easy.
-
Turn on Van De Graff on, let it build up charge. The charge is now stored on the Van De Graff. To
release the energy, touch it, you get shocked.
To make it mathematically easier to predict the exact charge, etc… We use a flat plate, to get a more
uniform E field.
All you need are two metal plates. Connect a battery (with a potential difference) to the plates. The potential
difference will cause electrons to flow onto one plate. The result is 1 + plate and 1 – plate.
Put the plates close together, and eventually when the charges build up enough, a spark will occur, and the
plates will be discharged, giving off their energy.
Do diagrams
So a capacitor generally will build up a certain amount of charge, then discharge, build up the charge again,
then discharge again. Different capacitors build up different charges and discharge them in different amounts of
time.
Do vandegraph capacitor demo
Original capacitors were called Lyden jars. It was a glass jaw with metal on the outside and metal on the
inside. A chain connected the metal on the inside to a metal ball on the lid. To charge, just touch the ball to a
charged object. To release the charge, touch both pieces of metal.
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Having two parallel plates takes up allot of space. However, industry has figured out a way to reduce the size.
They take two conducting sheets, place an
insulating sheet between them and simply roll it all up.
Do sheets of paper rolled up demo
Instead of using an air gap as the insulator between the plates, they use an insulating material called a
“Dielectric”
Different dielectrics are used in different capacitors to help regulate how much charge will build up and how
often it will discharge.
Capacitance is the ability of a conductor to store energy in the form of electrically separated charges.
The capacitance is given by the equation:
C = Q/V
It’s just charge per voltage
A Capitol Q is used to differentiate between a charged capacitor (Q) and any other charge (q)
Capacitance = magnitude of the charge on each plate / potential difference
The units are in Farads (Michael Faraday) F
A Farad is a big number. Usually we use Micro Farads. (10-6)
Another way to write it:
C = (epsilon 0) A/d
Epsilon 0 is the “permativity of free space”
It’s basically a constant. It is 8.85x10-12 C2 N/m2
A is the area of the plates
D is the distance between plates.
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Finally, its useful to see how much energy is stored in a capacitor:
EPE = ½ Q V
Q = charge on 1 plate (that’s why it’s ½ in front)
V = Potential Different
If you use the equation: EPE = ½ Q V
And substitute C = Q/V into it => Q = CV
You get
EPE = ½ CV2
Symbol for a capacitor:
Work on Capacitor Worksheet
Current
Current – The rate at which charge flows (the flow of charge).
This is just like current in a river, the rate at which water flows.
Water current would be defined at amount of water per time
Charge current is therefore defined as the amount of charge per time (q/t)
The symbol for current is “I”
I = q/t
Units : q/t => C/s => Ampheres
1 C/s = 1 A (amp)
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Since electrons transfer charges, lets look at how exactly electrons flow.
If there is NO potential difference, electrons wont be attracted in any particular direction (there is no net
positive to move toward).
However, they are still freely flowing in a conductor. They just don’t flow in any particular direction.
A good analogy is a Mosh Pitt at a rock concert. A crowd of people move around, bouncing in all
directions, but overall, do not move anywhere.
One can think of electrons as Moshing around a dance floor, randomly moving, but not moving in any
particular direction.
The electrons have an individual velocity, but the net velocity is 0
(Demo)
If there IS a potential difference, electrons, in their random moshing motion, will be attracted toward a specific
direction.
They will still randomly mosh around. However, they are now being pulled in one particular direction.
One can think of this as slightly tilting the dance floor of a mosh pit. People will still randomly move
around, but they will all slowely drift in one direction.
The electrons now have a Drift velocity, the net velocity is NOT 0.
Drift Velocity – The average velocity of an electron as it flows from high potential to low potential ( +
to -) Drift velocity is usually in the range of mm per second.
(Demo)
*** Although electrons move to create a current. When the concept of current was developed, scientists did not
know the electron carried the current. Therefore, they defined current as moving from + to -.
Current flows from + to –
Electrons flow from – to +
Types of Current
There are two types of current:
AC and DC
AC – Alternating Current
DC – Direct Current
Remember, current is just the moving of electrons along a conductor.
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DC
Nikola Tesla came up with dc current.
DC current is simple. This is what one would naturally assume how current flows.
The electrons drift steadily in one direction. “foreword”
I
t
Pro: Natural way current flows
Con: Requires extra energy to physically move the electrons along the conductor
(Not power efficient)
Ex: All batteries generate a D.C. Current
Since this is the natural way current flows, most electronic devices use DC current in their Circuitry
(tv’s, microwaves, computers, etc…)
AC
Electrons keep switching directions, sometimes going "forwards" and then going "backwards."
Overall, the electrons do not move anywhere. Their net velocity is 0. They just vibrate back and forth.
In the U.S. he vibration is standardized to 60 cycles per second. 60 Hz. In Europe it’s different.
Pros: More efficient (since you don’t need to waste energy physically moving the electrons)
Con: not natural. More complicated to use.
Ex: Power transmission is done via AC. Power from your wall outlets is AC.
However, since most devices use DC, the AC must be converted before appliances use it. This is usually done
by a transformer, a black box at the end of the plug, or a device inside the electronic appliance.
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Resistance
Resistance – The impedance of the motion of charge through a conductor.
Think of a river. Water flows downstream (gravitational potential difference), just like electrons flow
through a wire (electric potential difference).
However, in a river one can have trees, rocks, beaver dams, hoover dams, etc… all blocking the
flow of water, all impeding the flow of water.
Electrons can also have their flow impeded.
(Do water diagrams)
4 Factors that affect the resistance of the flow of charge.
1. l  R – Length – The greater length, the greater the resistance R.
2. A  1/R – Area – bigger area, lower R. (crossectional area)
3. T  R – Temperature – higher temp, higher resistance. (this is why superconductors need to be
extremely cold.
4. Type of Material – different materials have different outer electron shells, therefore, different materials
allow different amounts of electrons to flow.
Ex: aluminum has a high resistance for a metal
Copper has a low resistance for a metal
Gold has a VERY low resistance for a metal (delicate circuitry is made of gold.)
Formula for resistance: R = V/I
Ohm came up with this by experimenting with resistance.
We call this equation Ohms Law, although there are a few
in which the equation does not work.
Ohms Law: V = IR
V = volage (potential difference)
I = Current
Resistor – A device used to control the amount of current in a circuit.
The symbol for a resistor is:
Any object that gives off energy in a circuit gives off resistance.
For example, a hairdryer creates heat. A hairdryer can be thought of as a big resistor.
Toasters, TV’s, microwaves, computers, light bulbs, etc… can all be thought of as big resistors in a
circuit.
cases
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Light Bulb: A light bulb uses a special wire to create a high resistance. So high, that it glows.
The wire has a:
Small length
Large crossectional area
Made of a substance with a naturally high R
And is run at a High Temp.
These are the 4 factors that increase resistance.
Design:
It is a thin coil of wire that has a high current
running through it. It creates such a high resistance,
that the wire begins to heat up and glow, creating
light.
The wire is then incased in a sealed class envelope
with an inert gas pumped inside, inert so that the
wire does not catch fire (usually Argon gas)
Show a light bulb without the glass
Resistance worksheet
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Batteries
A closer look
Battery – a device that maintains a potential difference across their terminals by converting chemical energy
into Electrical energy.
A battery causes a chemical reaction where electrons
from 1 metal to another. This creates a separation of
charges, a + and -, which is a potential difference.
The catalyst for the chemical reaction is an acid.
(Diagram a battery)
There are various types of batteries, which give
different voltages and/or currents
It is easy to make a battery. All you need is two
different metals, and an acidic substance.
(Make fruit batteries)
flow
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Generator vs Battery
Battery – a device that maintains a potential difference across their terminals by converting chemical energy
into Electrical energy.
Generator - a device that maintains a potential difference across their terminals by converting mechanical
energy into Electrical energy.
We will look at generators in a later chapter.
Electrocution:
Current, not Voltage causes electrocution.
Voltage is just the difference of potential energy your body is at. This doesn’t affect anything.
However, current is the physical flow of electrons.
Having electrons flow through your body can be damaging because your body used a very low current to work
your muscles and nervous system. Any extra current will override the natural current in your body.
Enough current can cause your heart to stop beating, etc…
Your skin has a natural resistance. It lowers when it gets wet. So to look at the threat of electrocution, must
take into effect the voltage and the resistance of the body to determine the current.
Pass out and discuss Electrocution chart.
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POWER
Electrical Power:
Power is the rate at which work is done.
P = w/t = delta PE/ t
However, V is defined by PE/q => PE = qV
Substitute this in:
P = qV / t
However, what is q/t? Current, I
Therefore, P = IV
It is the rate at which charge looses PE. It’s being used to do work. Therefore it can also be thought of as the
rate at which work is done.
We can also use Ohms Law V = IR
P = IV = I(IV) = I2R
OR
P = IV = (V/R) V = V2/R
So we have 3 forms of Power. Which one you use depends on which information you know.
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Often we don’t use power to measure energy consumed. It’s a little easier for power companies to charge for
ENERGY used not POWER
They use what’s called a KWh (Kilowatt hour)
It’s the energy delivered in 1 hr at a rate of 1 Kw.
1 Kw h x (1000W / 1 kw) x (60 m / 1h) x (60 s / 1 m) = 3.6x106 w s
1 w = j/s therefore, w s = j
Therefore, 1 Kw h = 3.6x106 j
Power companies don’t charge for how much power they deliver, but for the energy we use.
On average, they charge 7 cents per Kw h.
Do examples:
How much does it cost to watch a 2 hr movie on a 90 W tv?
Energy saving bulbs vs regular bulbs, how much per year does it save you?
(Power Worksheet)