Electricity Electricity is the physical phenomena associated with the position or movement of electric charge. The study of electricity is generally divided into two areas electrostatics and current electricity. Electrostatics is the study of electric charge which is either at rest or jumping abruptly as in situations such as static electricity or lightning. Current electricity is the study of the steady flow of electric charge through wires in devices such as a radio or your house wiring. Electrostatics Two types of electric charge exist positive and negative. Negative charge is carried by the electron while positive charge is carried by the proton. Although these are both particles in an atom, only the electron is allowed to move. Protons are locked in the nuclei of atoms. In order to make an object have an overall charge of negative, extra electrons must be moved onto the object. In order to make an object have an overall charge of positive, electrons must be removed from the object (leaving more positive protons than negative electrons in the object). Like charges repel while opposite charges attract. The magnitude of charge is measured in Coulombs. For example, the charge of an electron is - 1.6 x 10-19 C and the charge of a proton is +1.6 x 10-19 C. Types of materials Materials can be classified by how easily they allow electrons to move through. Materials that completely restrict the movement of electrons are called insulators. Examples include rubber and glass. When excess electrons are placed onto an insulator, they remain in that location. Materials that allow electrons to move freely are called conductors. The best conductors are metals. Excess electrons placed on a conductor are free to move to any part of the conductor or to another conductor that is in contact with it. Other materials are classified as semi-conductors (allow movement of electrons under certain circumstances) and superconductors (allow movement of electrons without any friction or loss of energy). Charging an Object There are three ways to electrostatically charge an object friction, contact, and induction. Some materials, such as fur or carpet, contain atoms which do not bind their electrons tightly. When the fur is rubbed vigorously, electrons can be removed and deposited on another object such as a rubber rod. An insulator such as a rubber rod is used because excess electrons will remain on the rod and not spread off to your hand (like they would do if you were using a conducting rod). The fur will now be positivelycharged and the rod will be negatively-charged. Both objects have been charged by friction. If the rubber rod (which is negatively-charged because of the excess electrons deposited on it) is touched to an insulated sphere, the second object will now become negatively-charged since approximately 50% of the excess electrons on the rod will move to the sphere since they are repelling each other and can get farther apart. The sphere was charged by contact. An indirect way to charge an object is called induction. Imagine a metal sphere that is mounted above an insulated rod so it is electrically disconnected from the table. First, a net negative charge is placed on this sphere (A). A second sphere (B) is brought very close to it, but not touching. As a result, the electrons in sphere B will be repelled away from the negatively-charged sphere A. Sphere B will be positively-charged on the side near the sphere A and negatively-charged on the side that is farther away. Sphere B is now polarized. If you touch the far side of sphere B with your finger, many electrons will escape to your body. When you pull your finger away, sphere B will be left with a positive charge since it is missing negative electrons overall. Sphere B was charged by induction. Van de Graaff Generator Many electrostatics-related experiments can be conducted with a device called a Van de Graaff generator which builds-up a huge excess charge on a large metal sphere. -As a student s hand approaches the metal sphere, a spark will jump and a brief electrical shock will result. This occurs because the huge amount of charge on the metal sphere is ionizing nearby air (turning the air molecules into conductive ions). The ionized paths that form through the air are called leaders.
When the student s hand makes contact with one of the leaders, excess charge travels through the leader and onto the student. In this way, the charged particles are able to spread out more and alleviate some of the repulsion. The spark that is seen is due to the charged particles jumping abruptly through the air. The student will not be harmed, however, because the discharge is so brief. -If the same student stands on a milk crate and places a hand on the metal sphere before it is turned on, they will not be shocked. In this scenario, the student is slowly covered with excess charge at the same time as the excess builds-up on the metal sphere. Since there is no abrupt jump of charge, there is no discharge or shock. After awhile, the student s hair may begin to stand on end. This occurs because adjacent strands of hair become covered with excess charge and the charge repels the hairs apart. Lightning Lightning is actually an atmospheric electrostatic discharge. During a storm, clouds often become polarized. For example, the bottom of a cloud becomes negatively-charged while the top becomes positively-charged. The cloud then induces a charge on the ground and objects below. Over time, air molecules next to the cloud become ionized (turned into charged ions) by the strong charge on the bottom of the cloud. These charged air molecules ionize nearby molecules creating channels of ionized air called leaders. Leaders generally extend toward the ground, but they can have many branches. When one of the leader branches reaches the ground or an object on the ground, the electrical path between the cloud and ground is complete. Electrons will jump quickly through the leader. This huge discharge is the lightning flash. The thunder is caused by the air rapidly expanding outward as it is superheated by the electrons. Probability is highest that the leaders will connect with the tallest object on the ground first, but this is not guaranteed. Coulomb s Law It is possible to calculate the amount of force that attracts or repels two electrically-charged particles. The relationship is called Coulomb s law: F = kq 1q 2/r 2 where k is Coulomb s constant (9 x 10 9 ), q 1and q 2 are the charges on the two particles measured in Coulombs, and r is the distance in meters between the two particles. Sample Problem: What is the force between two electrons that are placed 8 cm apart? The charge on an electron is -1.6 x 10-19 C. Since F = kqq/r 2, F = (9 x 10 9 )(-1.6 x 10-19 )(-1.6 x 10-19 )/(0.08) 2 = 3.6 x 10-26 N Resistance When electrons flow through a conductive material, they experience many collisions with the metal atoms in the conductor, which produces resistance. As the length of a conductor increases, the electrons will have to travel further to reach the other end of the conductor, and will therefore experience more collisions, making it more difficult for them to flow through the conductor. Furthermore, if the conductor has a smaller cross-sectional area, charges flowing through it will experience more resistance. A rough analogy can be drawn to water flowing through a hose. A garden hose with a small cross-sectional area will produce more resistance and decrease the flow of water more than a larger fire hose. The resistance through a conductor can be calculated using the following equation: Where ρ is a constant known as resistivity, which depends on the type of conductive material, l is the length of the conductor, and A is the cross sectional area of the conductor. The values of resistivity for various materials can be found in the tables on the next page.
Resistivity Values at Room Temperature (20 C) Conductors ρ(ωm) Semiconductors ρ(ωm) Metals: Silver 1.47 x 10-8 Pure Carbon 3.5 x 10-5 Copper 1.72 x 10-8 Pure Germanium 0.60 Gold 2.44 x 10-8 Pure Silicon 2300 Aluminum 2.75 x 10-8 Tungsten 5.25 x 10-8 Insulators Steel 20 x 10-8 Amber 5 x 10 14 Lead 22 x 10-8 Glass 10 10-10 14 Mercury 95 x 10-8 Lucite > 10 13 Mica 10 11-10 15 Alloys: Manganin 44 x 10-8 Quartz (fused) 75 x 10 16 Constantan 49 x 10-8 Sulfur 10 15 Nichrome 100 x 10-8 Teflon > 10 13 Wood 10 8-10 11 Materials that have low resistivity are good conductors, meaning that they allow for electrons to flow easily through them. An insulator is a material the does not allow charges to flow freely through it, such as glass, rubber, or plastic. Notice that the resistivity values for insulators are significantly higher in the table above. A semiconductor is a material that has properties between those of insulators and conductors- under certain conditions, they can allow charge to flow freely. This makes semiconductors such as silicon or germanium very useful in electronic devices. Temperature will also influence the resistivity of a material. As the temperature of the material increases, the motion of atoms within that material will also increase, making it more difficult for charge to flow. This is similar to walking through a crowded room- it is easier to navigate through the crowd if everyone else is standing still, but becomes more difficult if they all start moving in random directions. It follows that if increasing temperature increases the resistance, then decreasing the temperature will decrease the resistance. The ultimate application of this can be seen in materials known as superconductors, which act as perfect conductors below a specific temperature. Unfortunately, the temperature needed for many superconductors to have no resistance is very close to absolute zero, so they are often not practical in everyday applications, although new uses for superconductors are continually being discovered. In theory, when the resistance of a superconductor drops to zero, there would be no energy loss. After reading the next few sections about current and voltage, come back and reconsider this. If there is no energy loss, a direct current could persist for years without an applied voltage! Circuits A circuit must contain at least a voltage sources (e.g., battery) and enough wire to connect the negative side of the battery to the positive side of the battery. Typically, a circuit will also contain one or more resistors (e.g., light bulb or speaker) and other components such as switches. In order for a circuit to be functional, there must be a complete circular path. Various components in the circuit such as a resistor can be wired in parallel or series. When batteries or resistors are wired in parallel they are connected end-to-end (+ to for batteries) with only 1 path through all the components. When batteries or resistors are wired in parallel, they are connected side-by-side (+ to + for batteries) to create multiple paths through the components. Voltage Batteries and generators create electrical potential differences by chemical reactions or physical means. Both devices pump electrons to create an excess of negative electrons at the negative
output and a deficit at the positive output. A greater build-up of electrons at the negative output yields more electrical pressure. When a wire or another conducting device is connected between the negative and positive outputs, electrons will move from the high electrical-pressure side (negative) to the low electrical-pressure side spontaneously. The measure of the difference in electrical pressure between the two outputs of a battery or generator is Voltage. Neither a battery nor a generator is the source of electrons in a circuit. These devices merely act as a pump that moves the electrons which already exist in the battery, wire, and any other conducting devices that are connected. When batteries are connected in series, the voltage are additive. When batteries are connected in parallel, the net voltage does not increase, but the life of all batteries is extended. Most household batteries have the same voltage (1.5V) regardless of size. AAA, AA, C and D batteries provide the same voltage, but D batteries have the longest life. 9V batteries are actually comprised of 6 smaller 1.5V batteries stacked in series inside the metal case. Households in the US are supplied with 120V. Resistance in Circuits We have already established that long and thin pieces of wire have more resistance than shorter thicker wires. Certain metals (e.g., gold and silver) have less resistance than others. Resistance is measured in Ohms which is assigned the symbol Ω. Resistors can be combined to make more or less equivalent resistance. When resistors are connected in series, they add together. When resistors are wired in parallel, the net resistance actually drops. This is because any additional (alternative) path provides an extra path to allow electrons to get from start to finish. An analogy could be a single lane or multiple lane highway. In a series circuit, all charge has to pass through one wire, similar to cars driving in a single lane. When multiple lanes are opened for traffic, the cars are able to travel faster. In a parallel circuit, there are multiple paths that the current will flow through, which allows current to flow faster and creates less resistance. Sample Problem: What is the equivalent resistance of two 8-ohm resistors and a 3-ohm resistor wired series? Answer: R eq = 8 + 8 +3 = 19 ohms. Current Current is a measure of the rate at which electrons flow through a circuit. Current is measured in amperes (or amps) which is equivalent to Coulombs/second. The current in any wire is a function of how much electrical pressure is pushing the electrons (Voltage) and how much resistance exists in the wire. In battery-based circuits, electrons travel all in one direction. This is called direct current or DC. In household circuits, electrons are constantly pushed forward and pulled back so that they never really leave the area of the wire where they began. This is called AC current. Currents are calculated using Ohm s law or V = IR where I = current. Sample Problem: What is the current in a circuit comprised of an 8-ohm resistor and a 4 Volt battery? Answer: V = IR or 4V = I(8ohm) so I = 0.5 A. Power Electrical power is a measure of how quickly a battery provides electrical energy or how quickly a resistor consumes it. Power is measured in Watts which is equal to Joules/second. The power provided by a battery will always equal the total power consumed by all resistors in the same circuit. Power is calculated by: P = IV for batteries and P = V 2 /R for resistors. Cost of Electricity Consumers are charged for electricity based on the kilowatt-hours they use. calculated by: C = 20 cents*kilowatts*hours where 20 cents is the rate in your town. The cost is
Electric Fields As explored earlier in this unit, an electric force can act on a charged particle through space without any physical contact. Most of the forces that we experience in everyday life are contact forces, meaning that objects have to physically touch to exert a force on one another. An exception to this rule has been gravity, which also acts at a distance. Both gravity and the electric force are field forces, in that they do not require contact for two objects to interact. An electric field exists in the region of space around any charged object. This electric field is what exerts an electric force on any other charged object that enters that region. This is a slight variance in what we discussed with Coulomb s Law in that the force does not come from the charged object itself, but rather from the field that the charged object produces. The magnitude of an electric field around a particle with charge q can be calculated using the following equation: Where k is Coulomb s constant, q is the charge of the particle, and r is the distance from the charged particle. Notice the resemblance to Coulomb s law- the only thing that is missing is the second charge. The electric field increases as the charge q increases, and decreases as the distance to the charge increases. Electric Field Lines The strength and direction of electric fields can be represented with electric field lines. The arrows on the lines indicate the direction of the electric field vector at any point. The number of electric field lines indicates the strength of the electric field at any point. Where there are a greater number of field lines per area, a stronger field is represented. Notice that the electric field lines point away from the positive charge and towards the negative charge in the diagram below. This convention is always used, as a positive sample charge will repel away from a positive charge along the direction of those field lines in the first diagram, and towards the negative charge as in the second diagram. Since both diagrams have an equal number of field lines, they are representing equal but opposite charge. Note: Field lines indicate that a positive sample charge moves away from positive q but towards (-q)
If the two charges above were placed near each other so that their electric fields could interact, the resulting field lines would curve away from the positive charge and back towards the negative charge. Note: The number of lines leaving positive is equal to lines meeting negative, so they are equal charge. In the electric field represented below, two particles with equal positive charge are placed near each other. Notice that the resulting field lines bend away from both particles, as a third positive particle would be repelled by both of the charges. Remember that areas with more field lines indicate a stronger electric field. Note: Where is charge greatest: A, B, C? In the following diagram, the positive particle has twice the charge of the negative particle. As a result, it produces a stronger electric field than the negatively charged particle, and when the two are placed near each other, it has greater influence on the resulting electric field. Notice that there are twice as many electric field lines originating from the positive charge than the negative charge.
As with gravity, there is also an electric potential energy. Similar to how work causes a change in gravitational potential energy, work would cause change in electric potential energy. Now, potential difference (voltage) does that work. The gravitational potential energy decreases as the distance from an object increases. In the same way, electric potential decreases as the distance to a point charge increases. The voltage at a given point can be represented on an electric field line diagram using an equipotential lines (or surfaces), which are the rings in the diagram below. All points on the same ring have the same voltage. The unit used to measure voltage is traditionally the volt. One volt is equal to 1 Joule/Coulomb. Another unit that is sometimes used is an electron volt (ev). One electron volt is defined as the kinetic energy gain by an electron accelerated by a potential difference of 1 V. Since 1 V = 1 J/C, 1 ev = 1.6 x10-19 C* V or 1.6 x 10-19 J.