General Outcome C1 - Students will explain field theory and analyze its applications in technologies used to produce, transmit and transform electrical energy.

Students will:
30–C1.1k define a field as a property of space around a mass, an electric charge or a magnet that causes another mass, electric charge or magnet introduced in to this region to experience a force
30–C1.2k compare the interaction between static electric charges with the interaction between magnetic poles and with the interaction between two masses at a distance
30–C1.3k compare the basic properties (source, direction and strength) of vector fields (gravitational, electric and magnetic), as determined by a test object
30–C1.4k describe gravitational and electric field strength at a given distance from a mass or a point charge, using the equations g = GM/r² and E = kq/r²
30–C1.5k describe the effect of a conductor moving through a magnetic field and inducing an electrical current
30–C1.6k describe the relationships, for up to three resistors, among power, current, voltage and resistance for series and parallel circuits, using the equations V = IR, P = VI, P = I²R, R_T = R₁ + R₂ + R₃, and 1/R_T = 1/R₁ + 1/R₂ + 1/R₃
30–C1.7k describe electrical energy in kilowatt hours and joules, using the equation E_e = Pt for electrical energy and the equation P = VI for power
30–C1.8k distinguish between alternating current (AC) and direct current (DC) in terms of electron flow and electric field
30–C1.9k describe the operation of a transformer, in terms of the relationship among current, voltage and the number of turns in the primary and secondary coils, using the equation N_p / N_s = V_p / V_s = I_s / I_p
30–C1.10k describe the advantage of AC over DC for transmitting and using electrical energy
30–C1.11k compare the general design and function of a DC electric motor and a generator
30–C1.12k describe, in terms of design and electrical energy, the functioning of safety technologies; e.g., circuit fuses and breakers, polarized plugs and ground wiring.

1.1 Field Lines

Fields

• Fields are 3-D region of space that exerts a force.

Electric fields

• Electric fields are a 3-D region of space that exerts a force on an electric charge.

There are 2 types of electric charge:

• Electrons are negatively charged
• Protons are positively charged

All object have protons and electrons in their atoms.

• Objects are neutral (zero charge) when the number of electrons and protons are the same and the positive and negative charges cancel out.
• Objects are negative when they have picked up extra electrons becoming net negatively charged.
• Objects are positive when they have lost some valence electrons becoming net positively charged.

Note: Charged objects only gain or loose a very very small percentage (< 1%) of their electrons. Charge can be transferred by rubbing two materials together. One material will take electrons from the other material.

• For example if you rub socks on carpet you can build up a charge and shock your siblings.
• For example if you comb/brush your hair in dry weather (winter) your hair will steal electrons from your hair. Your comb is negatively charged (steals electrons), your hair is positively charged (loses electrons).
• For example lightening storms are caused by clouds rubbing against air as the wind blows the cloud. Lightening is caused by air glowing white hot as electrons jump. Lightening can go from ground to cloud or cloud to ground depending on the charge or each.

Law of Electric Charges

• Opposite charges attract (positive attract negative and vice versa)
• Similar charges repel (positive repel positive; negative repel negative)

One electron has a charge of -1.60x10^-19 C
Electrical charge is measure in C, Coulombs.

Example:You have an electrical charge of 6.0 µC.
Answer

Voltage
Voltage, or electric potential difference measure the change in electrical energy between two points, based on the amount of charge transferred.

• A AA, AAA, C or D battery is at least 1.5 V
• A lantern battery is at least 6.0 V
• A car battery is at least 12 V
• A household outlet provides 120 V
• Rubbing your socks on carpet can build up 100 000 V
• A lightening bolt can be millions of volts

Example: A 12 volt car battery transfers 60 C of charge while starting a car. How much energy was used?

Insulators and Conductors

• Insulators do not allow electric fields to push electrons through them. It requires huge electric fields to move their electrons.
• Good insulators are non-metals because they have a tight hold on their outer valence electrons.
• This is why wiring is wrapped in plastic and circuits are made of silicon.
• Dry flesh is an excellent insulator.
• Conductors allow electric fields to easily push electrons through them.
• Good conductors are metals due to the way they loosely hold their outer valence electrons.
• This is why wiring is made of copper.
• Be careful with water as wet flesh is an excellent conductor. To be safe never touch live electrical wires.

Electric Fields

• We can draw the electric fields around charged objects. Electrical field lines always start on positive charges and finish on negative charges. It shows the way a small positive test charge would move in the field.
• The closer the lines, the stronger the electric field.
• Electric field lines never cross. If they did the small positive test charge would have to make a choice and test charges don’t have brains.
• Non-uniform electric fields between spherical charges. The field strength changes depending where you are.
• A parallel plate apparatus is often used because it provides a uniform electric field The field is the same everywhere between the plates and there is no field outside of the plates.
• Note: there is a little variation in the field at the edges of the plates but it is not significant.

Gravitational field

• Gravitational field is a 3-D region of space that exerts a force on a objects with mass.
• We have only ever observed gravity as an attractive force, never a repulsive force. Scientists would love to find something with negative mass.
• Gravitational field lines show the direction a mass falls. They point towards the largest closest mass.
• In between is a neutral point where the forces cancel and you don’t accelerate either way (Lagrange point).

Magnetic Fields

• Magnetic fields are a 3-D region of space that exerts a force on a magnetic pole.
• There are 2 types of magnetic poles
• North poles (point to the geographic north pole)
• South poles (point to the geographic south pole)
• Just like electric charges, opposite magnetic poles attract and like magnetic poles repel.
• Magnetic field lines are always loops the go away the north pole and towards the south pole. Inside the magnet the loop continues from the south to the north (dotted lines).
• Only a few elements stay magnetic. They are found together on the periodic table.
• We make most magnets out of iron, cobalt and nickel. Strong rare earth magnets are made of iron and neodymium or cobalt and samarium. The other elements are simply too expensive.

1.2 Equations for Fields

Gravitational Field Strength

• g – gravitational field strength, N/kg
• G – gravitational constant 6.67×10^-11 Nm²/kg² (don’t write out, use G)
• m – mass of source of field, kg
• r – distance from source, m

|E| =	kq	→
	r2

• E – electric field strength, N/C
• k – coulomb’s constant 8.99×10⁹ Nm²/C² (don’t write out, use k)
• q – electric charge, C
• r – distance from source, m

1.3 Motors and Generators

Engines burn a fuel in order to change chemical potential energy into kinetic energy. For example piston engines in cars and boats, turbine engines in helicopters and airplanes, rocket engines in rockets and space shuttles as well as experimental aerospikes, scram jet, etc… Motors use electrically powered magnetic fields in order to change electrical energy into kinetic energy. For example vacuums, blenders, headphones/earphones, electric cars, large ships, large dump trucks (Fort McMurray), etc… Electric motors have several advantages over engines.

	Electric Motor	Engine
Number of moving parts	One (armature)	Tens to hundreds (pistons, valves, gears, cams, springs, etc…)
Power	Instant	Needs high RPM (revolutions per minute)
How it works	Magnetic fields pushing on each other.	Burning gases expand pushing on metal (piston or turbine blade)
Efficiency	High (80 to 90%)	Low (10 to 40%)

How a motor works

• When a wire has a current (electrons, electricity) moving through it, the moving electrons create a magnetic field around the wire.
• If you have more wire than you get a stronger magnetic field.
• If you put a current carrying wire in another magnetic field, the two fields push on each other and cause the wire to move.
• We use the magnetic fields pushing on each other to force a coil of wire (armature) to turn (spin).
• Electric motors are being used in more and more places because with modern electronics, the speed of the movement, how much it moves and how much force it pushes with can be very carefully controlled.

Generators

• Generators are exactly the opposite of motors. They change kinetic energy into electrical energy. The generator can be turned by an engine (alternator in car), or a turbine (hydroelectric dam, nuclear reactor).
• The parts of a generator are exactly the same as a motor. Electric cars take advantage of this to be more efficient.

Accelerating and driving are similar for gasoline and electric.
Chemical Energy fuel	→	Gasoline Engine convertor	→	Kinetic Energy moving
Electrical Energy battery	→	Motor/Generator convertor	→	Kinetic Energy moving
Decelerating and stopping is where electric drive systems are very different.
Kinetic Energy moving	→	Brakes convertor	→	Heat waste energy
Kinetic Energy moving	→	generator/Motor convertor	→	Electrical Energy battery

There are two types of electric motors and generators:
Direct Current
The electricity only goes in one direction. Provided by batteries.
Alternating Current
The electricity changes direction. Household electrical power.

1.4 Electric Circuits

Circuit Schematic diagram
A diagram of the parts of an electrical circuit using symbols for the parts.

Part	Schematic
battery
switch
ammeter
voltmeter
light
resistor

Electric circuits

• There are two types of electrical circuits:
• Series circuit – a single path for electrons to get through the circuit.
• Parallel circuit – multiple paths for electrons to get through the circuit.

Measuring Electric circuits

• There are two types of electrical circuits:
• Voltage – the energy between two points in a circuit. The energy changes as the electricity goes through the parts of the circuit. The voltmeter must always be connected to the start and end of a resistor or battery.
• Current – the amount of charge (# electrons) flowing through that part of the circuit. Think of this as a turn still that counts electrons going through the circuit. It must replace a wire, and be part of the circuit.
• Using an ammeter and a voltmeter at the same time. All the current flows through the ammeter. The voltmeter measures the voltage drop across the light.

Resistance

• A measure of how difficult it is for current to flow. More resistance means less current will flow.
• A resistor is something in the circuit that uses energy, uses voltage (light, fan, heater). We use a zig zag symbol.

Ohm's Law

R =	V
	I
I =	V
	R
V =	I × R

• V - voltage, V
• I - current, A
• R - resistance, Ω

Example: A 4.5 volt battery in a flashlight powers a 9.0 Ω LED. What is the current in the flashlight?

Analyzing Circuits

Voltage

• Think of voltage as energy.
• Going through a battery increases the voltage (energy).
• Going through a light or resistor decreases (uses) the voltage (energy).
• The voltage in (battery total) must be equal to the voltage out (light, resistor total).

Voltage in Series
In a series circuit the electron loses energy in each light or resistor. The total voltage is divided between each resistor.

Voltage in Parallel
In a parallel circuit the electron only goes through one resistor branch. The voltage is the same across each resistor.

Resistance

Resistance in Series
A series circuit means that the electrons have to go through each resistor, so more resistors increases the total resistance.
R_Total = R₁ + R₂ + R₃

Example: Use the following circuit diagram.
A. What is the total resistance of this circuit?
B. If the current is 2.0 A, what is the voltage supplied by the batteries?



Example: Find the voltage across each resistor. The battery provides 12 volts.
Resistance in Parallel
A parallel circuit means that the electrons have many path to get across resistors making it easier to move, so more resistors decreases the total resistance.

1	=	1	+	1	+	1
RTotal		R1		R2		R3

Example: The following circuit is powered by a 9.0 volt battery.
A. What is the total resistance of the circuit?
B. What is the current leaving the battery?



Example: The circuit is powered by a 12 V battery. What is the current in each resistor?

1.5 Transmitting Electrical Energy

Power is a measure of how quickly an energy converter can change one type of energy to another type of energy. In the metric system power is measured in Watts, the SAE unit is horsepower. We see this with light bulbs. Less watts of power means it uses less energy and is more efficient

Power =	Work (energy)
	time
P =	W
	t

• P – power, J/s
• W – work or energy, J
• t – time, s

Example: A Tesla car’s electric motor has a power rating of 615 kW and can accelerate from rest to 100 km/h in 2.8 s. How much energy does it convert from electrical to kinetic while accelerating?


Power of a Circuit
There are three ways to calculate the power of an electric circuit.

P =   IV	P =   I2R	P =	V2
			R

• P – power, W or J/
• R – resistance, Ω
• V – voltage, V
• I – current, A

Example: A blender is plugged into a household circuit (120V) and draws a current of 1.5 A. What is the power of the blender?

Example: In the following circuit the battery provides 6.0 V, and the resisters are 6.0 Ω and 8.0 Ω respectively. What is the power in the following circuit?

Example: The following circuit has a current of 3.0 A, and has a 6.0 Ω and 8.0 Ω resistor respectively. What is the power of the following circuit?

Electrical Transformer

• The purpose of a transformer is to change the current : voltage ratio while the power (energy) stays the same. It is efficient to send electric power with very high voltage (250 000V)and low current, but it would be extremely dangerous in a household circuit, because electricity would arc out of the outlet. We use a transformer near your house to change the very high voltage to low voltage (120 V) using a transformer.
• House hold electricity is alternating current so that we can use transformers, which will not work with direct current.
• We know that current carrying wire have a magnetic field around them, but to get a current to flow in a wire we need a changing magnetic field.

Np	=	Vp	=	Is
Ns		Vs		Ip

• N – turns in the coil of wire
• V – voltage, V
• I – current, A