ELECTRICITY AND MAGNETISM

Electric Charge and Current

All matter is made of positive particles called protons and negative particles called electrons. In order to create an electric charge, electrons must be separated from neutral atoms which have an equal number of protons and electrons.This results in two charges. The atoms which lost electrons are now positive since they have more protons than electrons. The electrons that have been removed give the object that removed them a negative charge since it now has more electrons than protons.The third atomic particle we will discuss in more detail later is the neutron which has no chrge and has about the same mass as a proton.

The unit of electric charge is called the coulomb. 6.25 x 1018 electrons or protons are contained in 1 coulomb of charge.

Electric current is defined as the time rate of flow of electric charge. The equation used to calculate current is:

I = q/t

where I is current in amperes, q is amount of charge in coulombs, and t is time in seconds. The basic unit of current, ampere(A) is one coulomb per second. Sometimes ampere is shortened to amp.

Example

Find the magnitude of the electric current if 4.8 x 1018 electrons pass by a point in a wire during .25 seconds.

Currents flow easily through materials that are good conductors. Good conductors have loosely bound electrons that are able to move easily. Metals are good conductors since they have electrons that are not bound to any one specific atom.Materials in which nearly all of the electrons are tightly bound are called insulators since they do not conduct electric currents very well. Examples are wood, glass, and plastics.Materials which are intermediate conductors(neither good nor bad) are called semiconductors. Graphite and silicon are examples.

Electric Force

Any two charged particles will exert an electric force on each other. The nature of these forces is stated by the Law of Charges:

Like charges repel, unlike charges attract.

Two negative charges or two positive charges repel each other. A positive and negative charge will attract.

The magnitude of the electric force is determined by Coulomb's Law.

The force between two charged bodies is directly proportional to the product of the magnitudes of the charges and inversely proportionasl to the square of the distance between them.

The equation for this is:

F = kq1q2/r2

F is the magnitude of the force, q1 and q2 are the magnitudes of the two charges, r is the distance between the charges, and k is Coulomb's constant with a value of 9.0 x 109 Nm2/C2.

One important thing to remember is that electric forces are much stronger than gravitational forces involving similar sized particles.

Example

Find the force on two charges of +0.50 C and +2.0 C if they are separated by a distance of 3.0 m.

Objects can be charged by conduction or induction. With charging by conduction, a charged object is brought in contact with an uncharged object. Electrons flow from negative to neutral or from neutral to positive to neutralize as much charge as possible.

With charging by induction, the charged object is brought near the uncharged object creating regions of positive and negative charge within the uncharged object.

Objects can also be charged by friction. Electrons may be transferred from one object to another when they rub together. An example would be the charge you receive and the spark that jumps between your hand and a doorknob as you walk on a carpet. Static generated in a dryer is another example.

Voltage and Electrical Power

Electric potential energy is defined as the work done in separating charges. Since work must be done to separate charges, we get energy back if we allow them to get back together.Potential difference or voltage is defined as the amount of work or energy per unit of charge required to move a charge between two points.The unit is the volt(v) which is one joule per coulomb(j/c).If the potential difference is 6v, you get 6 joules of energy out when 1 coulomb of charge moves between the two points.The equation for voltage is:

V = W/q

where V is voltage, W is work or energy in joules, and q is the charge in coulombs.

Example

To separate 0.25 C of charge from another charge, 30 j of work is done. Find the electric potential energy of the charge. What is the voltage generated?

A voltage will cause a current to flow between two points on a conductor. When this happens, there is an opposition to the current flow called resistance. The unit of resistance is the ohm(Ω) and is equal to 1 volt per ampere.

Ohm's Law relates voltage, resistance, and current in the equation:

V = IR

where V is voltage, I is current, and R is resistance.

Example

If a component with a 50 ohm resistance is connected to a 120 v source, how much current flows through the component?

The parts of a simple electric circuit are shown in the following diagram. On the left we have a drawing of an electric circuit and on the right we have a circuit diagram.

The circuit is said to be open if there is no direct connection at the switch so that current cannot flow. If the connection is made so that current can flow, the circuit is said to be closed.

Before electrons were discovered, it was believed that electric currents consisted of movement of positive charge. Because of this misconception, conventional current is said to flow from the positive terminal to the negative terminal. Most devices are negatively grounded. This does not affect the energy transfer, only the concept of how it is transferred.

Electric power is defined as work per unit of time just like mechanical power. The equations, however, are different since we must write them in terms of voltage, current, and resistance. The equations are:

P = IV

P = I2R

Example

A car radio draws 0.25 A of current in a 12v system. (a)Find the power the radio uses. (b)Find the resistance of the radio.

The unit of power is the watt and most electric devices other than electric motors are rated in watts or kilowatts.

Simple Electric Circuits and Electrical Safety

The two types of electric current are DC and AC. DC stands for direct current which means the current only flows in one direction through the circuit. DC is supplied by batteries and rectifiers.AC stands for alternating current and means that the current changes direction in the circuit. In the U.S. this changing current is called 60 cycle or 60 hz AC since it completes 60 cycles of positive and negative direction each second.AC is produced by the power companies and is the electric energy we use in the home to provide energy to most devices.

The two basic ways to connect parts of a circuit are series and parallel.In a series circuit, the current flows through one component after another following just one path. The current is the same in all parts of the circuit.Each component uses up some of the voltage so that the total voltage across the circuit equals the sum of the individual voltage drops.The circuit below shows three light bulbs wired in series with a battery and each other.

To find the total equivalent resistance in the circuit, we simply add together the magnitudes of all of the individual resistances.

Rs = R1 + R2 + R3

If we were to replace all of the resistances in the circuit with an equivalent resistance Rs, then the total current in the circuit would not change.

Example

A student connects a 10 ohm resistor, a 15 ohm resistor, and a 20 ohm resistor in series and connects them to a 50 V DC voltage source. Find the current in the circuit and find the power expended in the circuit.

The disadvantage to this type of circuit shows up if one component fails. Like some Christmas lights, if one bulb burns out, this opens the circuit so that current cannot flow in any part of it. In that case they all go out.

Parallel circuit wiring is usually much more convenient. In parallel wired lights, if one goes out, the rest remain lit.

In the parallel circuit shown above, three light bulbs are wired in parallel. The current from the battery does not need to go through one of the bulbs to get to the others. If one were to burn out, each of the other bulbs would still form a complete circuit and continue to produce light.In this circuit, the voltage is the same across each component since they are all connected to the voltage source at the same point.The total current is equal to the sum of the individual currents and this allows us to derive the formula for the equivalent resistance in a parallel circuit.

It = I1 + I2 +I3

Vt/Rt = V1/R1 + V2/R2 + V3/R3

since Vt, V1, V2, and V3 are all the same, they divide out of the equation leaving:

1/Rt = 1/R1 + 1/R2 + 1/R3

Rt is called the equivalent resistance for the circuit. It can replace the other three resistors without affecting the total current or power dissipation in the circuit.The number of resistances in the circuit is not limited to three. It can vary from 2 up to theoretically an infinitely large number.

Example

A student connects a 10 ohm resistor, a 15 ohm resistor, and a 20 ohm resistor in parallel and connects them to a 50 v battery.Find (a) the current in the circuit and (b) the power expended in the circuit.

When resistances are wired in parallel, the equivalent resistance is always less than the value of the smallest magnitude resistor in the circuit.

Household circuits are wire in parallel for two main reasons.1. The same voltage is available at every connection in the house. 120 volts is the potential difference between a "hot" wire and the ground(zero potential wire). Since there are two incoming potentials, one at +120 v and one at -120 v, air conditioners, clothes dryers, etc. can be wired across these two legs to give a potential difference of 240 v.

In the diagram above, we can see how we get 120 v for small appliances and 240 v for large ones.

2. If one appliance is turned off or fails, the others in the circuit will continue to operate. Refer to the diagram above to see how this is true.

Electrical Safety

A fuse can be used to protect a circuit from overload. A fuse is a device which is wired in series with the circuit it is protecting and consists of a conductor which will melt when its maximum current rating is reached. This acts like a switch that opens the circuit and the current cannot become large enough to damage the circuit.Fuses are used in automobiles, audio equipment, and other devices such as microwave ovens. Fuses may be found in the household circuits for some older homes. Houses built since 1970 or so will have circuit breakers instead of fuses. A circuit breaker is an automatic switch which is said to "trip" or open the circuit when the current gets too high.Circuit breakers and fuses generally allow a maximum of 20 or 30 amps to flow through an individual circuit.

Another hazard of using electrical devices is the risk of electrical shock. If a hot wire in a device contacts a metal part then a person touching this part can receive a shock.

In the diagram above, the person is being shocked even though there is a fuse in the circuit and one wire goes to ground. The person becomes a parallel component to the resistance within the device and receives a signifigant amount of current.

In this diagram, the metal casing has a separate grounding wire with very low resistance. This person is not shocked since the current flows through the dedicated grounding wire.Another type of grounding system uses polarized plugs. One prong on the plug and one hole in the wall socket are larger than their counterparts. This is to ensure that you plug the ground wire prong into the grounded side of the outlet. This works OK as long as there are no errors made in the wiring of the socket or the polarized plug.

The three prong plug is safer since the ground wire under normal conditions carries no current.

Magnetism

A material called lodestone was discovered by the Greeks in a region of Turkey called Magnesia. Lodestone was used as the first form of a compass beginning in the twelvth century AD.

Lodestone will align itself with the earth's magnetic field because there will be two regions on the stone where its magnetic strength is most concentrated. These regions are called magnetic poles.

The north pole of a magnet is actually a north seeking pole since it points north when allowed to freely turn. The same is true for the south pole.

The concept describing the interaction of the poles of two magnets is called the Law of Poles and it states:

Like poles repel, and unlike poles attract.

The strength of the force depends on the strength of the poles and is inversely related to the square of the distance between them.

All magnets are dipoles(they have 2 poles). A magnetic monopole would consist of a N or S pole without the other. No magnetic monopole has ever been observed.

A magnetic field is a region of space where a magnetic force is experienced by a magnet or a ferromagnetic material(iron, cobalt or nickel). Magnetic fields can be mapped by using a small compass or iron filings.

Magnetic forces are thought to exist as a result of moving or spinning charges. There is always a magnetic field associated with any electric current. The strength of the magnetic field force depends on the size of the current. A coil of wire wrapped around an iron core is called an electromagnet and can be turned on and off as needed.Permanent magnets are materials in which electron spin causes magnetic effects. Most materials are not magnetic because their electron spin directions are oriented randomly and cancel each other out. In certain elements(iron, cobalt, nickel), a signifigant number of electron spins can be generally aligned. The areas of alignment are called magnetic domains. If enough of these domains can be aligned, then the substance becomes a magnet.

The Earth's Magnetic Field

In the seventeenth century William Gilbert proposed the idea that the earth acts like a huge bar magnet. The poles of this imaginary bar magnet are located near the earth's geographic north and south poles.The earth's magnetic field exists because of movement of charged particles within the earth as it rotates. Since earth's magnetic north does not coincide with the earth's geographic north, a correction must be made in determining north with a compass. This correction is called magnetic declination which is the angle between true north and magnetic north. Declination changes as you move to the east or west.

Electromagnetism

Electromagnetism is defined as the interaction of electric and magnetc effects. The two main principles are :

1. Moving electric charges(current) give rise to magnetic fields.2. Magnetic fields can deflect a moving electric charge.

An example of this interaction occurs in a telephone. The microphone in a telephone converts sound energy into motion of a diaphragm and then into an electrical signal that travels through wires or as radio waves to a reciever which converts the electrical signal back into sound in a speaker that vibrates when its magnet interacts with the electric current.

Electric motors convert electrical energy into energy of motion. An electric current passes through the armature composed of loops of wire oriented between two magnets called field magnets. These loops are repelled by both magnets and begin to turn. At just the right time, the split ring commutator causes the current to change direction so that the loops are still repelled by both magnets. As long as electricity is supplied to the armature, the motor will continue to turn.

This is called a DC motor since it uses batteries or some other source of DC current. An AC motor works differently and uses household current.

A generator is a device that converts mechanical energy into electrical energy. It uses the principle of electromagnetic induction. Electromagnetic induction occurs when a conductor and a magnet are in motion relative to each other.

A generator produces either DC or AC voltage depending on the internal construction of the generator. Most electricity is generated as AC and is converted to DC with a rectifier as needed.

One advantage to the use of AC voltage is its ability to be stepped up to a higher value or stepped down to a lower value.

AC can then be transmitted over great distances at higher voltage and lower current to avoid energy losses and then stepped down to the 120 - 240 volts we use in households.

The device that does this is called a transformer and is made of two separate coils of wire wrapped around a ferromagnetic metal core. Changes in current in the primary coil(input voltage) causes a changing magnetic field to exist. This changing magnetic field induces a current in the secondary coil(output voltage). The output voltage can be more(stepped up) or less(stepped down) than the input voltage and depends on the ratio of the number of turns of wire in the primary compared to the number of turns in the secondary.

The voltage change for a transformer can be found using the equation:

V2 = (N2/N1)V1

where V2 is the voltage in the secondary circuit, V1 is the voltage in the primary circuit, N2 is the number of turns in the secondary coil, and N1 is the number of turns in the primary coil.

Example

A transformer has 300 turns in its secondary and 100 turns in its primary. The primary is connected to a 12 v source.(a) Is this a step up or step down transformer?(b) What is the secondary voltage?(c ) If the transformer is 100% efficient, the power in the primary equals the power in the secondary. If 2.0 A flows in the primary, find the current in the secondary.