# Electricity

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1 Electricity Electric Charge There are two fundamental charges in the universe. Positive (proton) has a charge of x C Negative (electron) has a charge of 1.60 x C There is one general rule for electric charges: Likes repel and opposites attract When objects have equal amounts of each they are said to be NEUTRAL. If it has excess electrons it has a negative charge, excess protons it has a positive charge There are many ways in which to move charge. One way is through friction. When an object builds up a charge this is called STATIC ELECTRICITY because the electrons are not moving. If you rub your hair with a balloon, electrons from your hair are transferred to the balloon giving it a net negative charge, leaving your hair a net positive charge. Since they have opposite charges they then attract one another. See pictures below: If the oppositely charge objects come in contact with one another then the electrons will jump from one object to the next. You see this as a spark. You don t tend to see this DISCHARGE (transfer) of charge in South Florida very much because of the humidity. Water molecules in the air provide a path for electrons to flow so the object has a hard time keeping a charge. Electric charge is quantized In 1909 Robert Millikan discovered that there is a fundamental unit of charge, e (1.60 x C), and that every charged object had a charge that was a multiple of this charge. See picture below: 1

2 The unit for charge is the Coulomb (C) C = 6.2 x 1018 electrons All substances are placed in four categories: Insulators - These do not allow electric charges to move freely. (air, rubber, glass, organic materials) Semiconductors - In their pure state they act like insulators but when impurities are added, they greatly increase their conductivity. (metalloids) Conductors - These substances allow electric charges to move freely. (metals, electrolytes) Superconductors - They become PERFECT conductors when they are at or below certain temperatures. (alloys) How are objects charged? 1) CONTACT (Friction) - As discussed before this happens when the surfaces of the objects are rubbed together. (Conductor or Insulator) Ex: Balloon and Hair, Glass rod and Wool. 2) INDUCTION A) Conductors i. In this process a charged object is brought close to a neutral object causing a polarization at the surface of the object. The object is then disconnected from the ground and a net charge is left on the object. See pictures below: B) Insulators ii. In this process a surface charge is induced on insulators by polarization. There is a realignment of the molecules/atoms charges after a period of time or a discharge. See picture below: 2

3 Coulomb s Law Charged objects will apply a force, attractive or repulsive, on one another. The closer the two charges are the greater the force between them. q F electric = k 1 q 2 N m 2 c k r 2 c = 9.0x10 9 C 2 Remember that forces are vectors and they must be added as such (pay attention to direction). The electric Force is a field force; therefore no contact is necessary. However, this force can be negative or positive. If it is negative that means that the force is ATTRACTIVE and positive means that it is REPULSIVE. This field force is much stronger than gravity, however it does follow the same pattern (Inverse square law). Charles Coulomb quantified the electric force using a torsion balance. See below: Electric Field Electric fields exist in the region of space around charged objects. When these fields interact they produce ELECTRIC FORCES. An electric field can be defined according to the following equation: E = F electric q When defining an electric field you must understand that it can be done in a myriad of ways. When using the above equation we are assuming that a test charge is placed in the field of another charged object. Therefore we are speaking of the electric filed strength of the charged object and NOT the test charge. In addition the equation above is quantifying the electric field strength at a single given point (wherever you place the point charge) See pictures below: Another major assumption in this definition is that the test charge has a value small enough that it does not cause a redistribution of charge on the object creating the electric field. See below: When discussing the magnitude of the Electric Field strength from a point charge the equation reduces to: E = k q r 2 k c = 9.0 X 10 9 N m 2 / C 2 3

4 Electric fields are VECTORS. Therefore in order to calculate the electric field strength due to numerous charges you must use the superposition principle. Electric Field Lines Even though these lines don t really exist they are a convenient way for us to visualize Electric Fields in space. When drawing electric fields lines use these general rules as a guide: A) For positive charges arrows are drawn outward and for negative inward. B) Lines are drawn perpendicular to the charge s surface. C) The number of lines drawn is proportional to the magnitude of the charge. D) Field lines CANNOT cross. See examples below: Electrical Potential Energy This is the potential energy due to the placement of a charge in an electric field. So you may think of it like gravitational potential energy. Indeed electric potential energy should be included when discussing the mechanical energy of a system. M.E. = K.E. Translational + K.E. Rotational + P.E. Gravitatinal + P.E. Elastic + P.E. Electric Uniform Field In order for a charge to be moved in a field some work must be done. This work corresponds to the change in electric potential energy. We can therefore derive the following equation: W electric = ΔPE electric = qeδd = qδv Unit: Joule (J) This equation only works for a uniform field. When field strength and direction is the same throughout the field. Also the displacement must be in the direction of the field. If the charge is moving in the direction of the field it has a positive displacement. If the charge is moving against the field, it has a negative displacement. 4

5 See picture below: Non-uniform Field A non-uniform field is created by point charges. Therefore we must calculate electric potential using another expression. PE elec = k q 1 q 2 r k c = 9.0 X 10 9 N m 2 / C 2 Notice that it is very similar to the electric field force. NOTE: For both cases motion that is perpendicular to the electric field does not affect electric potential. ELECTRIC POTENTIAL Unfortunately, as the value of a charge changes so does the electric potential energy of that point in an electric field. Therefore it is easier to speak in terms of electric potential. Electric potential gets rid of the influence of the charges value. Therefore no matter what the charge, the electric potential of the field is the same and independent of the charge. However, most of the time you don t speak of electric potential but of potential difference (voltage). This is the change in electric potential. ΔV = ΔPE elec q Unit: Volt (J/C) A) Uniform Field ΔV = EΔd B) Potential Difference Between a point at infinity and some location near a point charge V = k q r k c = 9.0 X 10 9 N m 2 / C 2 5

6 CAPACITANCE Capacitors are used in many electronic devices. A capacitor has the ability to store charge. A typical type of capacitor is called a parallel plate capacitor. See below: Capacitance measures the ability of a conductor to store energy. There are two equations that we are going to use in order to store charge: Generally, C = Q ΔV (Q total charge) For a parallel plate capacitor, C = ε 0 A d ε 0 = 8.85x10 12 C 2 N m 2 (permittivity) Earth actually acts as a large capacitor. Due to its size it can hold an immense amount of charge. In other words it can give and accept a large amount of charge without it s electric potential changing too much. This is why the earth is use as the ground in circuits. By placing a dielectric, an insulator, you can change the capacitance of a capacitor. This is because the molecules in a dielectric can rotate so that there is an excess negative charge near the surface of the dielectric at the positive plate and an excess positive charge near the surface of the dielectric at the negative plate. See picture below: 6

7 Discharging capacitors rapidly release their charge. The charged capacitor has electrical potential energy because it takes work to move the charges through a circuit. It can be calculated by the following equation: ΔPE = 1 2 QΔV = 1 2 CΔV 2 = 1 2 Q 2 C Unit: Joule ELECTRIC CURRENT Current is the rate of movement of charge. However, when speaking of current we say that positive charges are moving through a cross-section of a given area. See below: I = ΔQ Unit : Ampere (A) ΔT Positive and negative charges in motion are called charge carriers. It is the potential difference that causes the charge carriers to move. Electrons in metal and ions in solution are good conductors because they have charge carriers that are freely able to move. A potential difference is applied to a conductor by setting up an electric field. This electric field travels through the conductor at the speed of light. One major misconception is that electrons move at the speed of light through the conductor. The drift velocity tends to be relatively small about 2.46 x 10-4 m/s. See picture below: Batteries and generators provide a current by maintaining a potential difference between the ends of a circuit. These devices provide electrical energy to the current and in turn the current provides the energy to the electrical device. Current can be direct (DC) or alternating (AC). Batteries produce direct current. The movement of charge is in ONE direction. Generators can produce DC or AC. In AC the poles of the generator constantly change sign (+ to- and back). If this happened slowly in a light bulb you would see flickering. However, in the US this is done at 60 Hertz. So the change is quick enough that you can t detect it. The power supplied to our homes is AC. AC is used due to the fact that it is easier to distribute and manipulate. RESISTANCE The impedance of the motion of charge through a conductor is the resistance of the conductor. It can be calculated using Ohm s Law: R = ΔV Unit : Ohm I Not all materials follow this law. Substances that have a constant resistance over a range of potentials are ohmic, those that do not are non-ohmic. See graphs below: 7

8 The resistance of a material depends on the length, cross-sectional area, material, and temperature. See chart below: VOLTAGE Voltage is the electric potential energy per unit charge measured in volts (joules per coulomb). Voltage is a property of an electric field, not individual electrons. V = IR Unit: Volt (V) Since the voltage is usually the constant in electric circuits, resistors are used to control the current in a circuit. Currents greater than 0.15 Amps can kill a human. Superconductors are special because for temperatures below the critical temperature they have zero resistance. Therefore once a current is set up in them the potential difference can be removed and the current is still present. Electric Power Electric Power is the rate at which charge carriers do work. It can be calculated by P = IΔV = ΔV 2 R = I 2 R Unit: Watt (W) (1 J/s ) Energy is used to power electrical devices. However some of that energy is also converted into internal energy (heating of the electrical components) and this is called joule heating or an I 2 R loss. Power companies charge for energy not power. The unit Kilowatt-hour sounds like power but it isn t. 1 kw h W 1 kw 60 min 1 h 60 s 1min = W s = J When transferring electrical power the company wants to minimize the I 2 R loss and maximize the amount of energy it can deliver. It can do this by decreasing the current or resistance. The resistance only gets larger due to the fact that the power lines increase in length. So the only other option is to transfer the electricity at a very small current. The problem is that the power would decrease. So the power company sends the current at a very high voltage. Usually the voltage goes from 765,000 across power lines to 4000 at local transformers to 240/120( ) V at your house. 8

9 Circuits and Schematic Diagrams In order for perople to be able to communicate with one another a schematic code was developed for various circuit components. See chart below: Schematic diagrams are representations of electric circuits. They are circuit diagrams. In order to have an electrical circuit there must be a path for the charges to follow. Any device that dissipates energy is called a load. A circuit is said to short circuit when there is no load present in the circuit. This is dangerous because the current will increase causing wires to overheat and start fires. This is why circuit breakers are installed in homes. When too much current starts flowing through a circuit, the circuit breaker pops before the wires get hot and start a fire. When current is able to flow through the circuit it is said to be closed and when it can t it is said to be open. The power source in a circuit (battery/generator) is also called the emf, electromagnetic force. Due to the internal friction of a battery its terminal voltage is always less than its emf. 9

10 A) Series Circuits In these circuits there is only one path for the current to flow through. See picture below: We have some general rules 1) Current is the same 2) Resistance add or R eq = R 1 + R 2 + R 3. 3) Voltage adds up to the terminal voltage B) Parallel Circuits In these circuits there are many paths for the current to flow through. See picture below: We have some general rules 1) Current adds in parallel I = I 1 + I 2 + I 3.. 2) Resistance is according to the following 1 = or R R eq R 1 R 2 R eq = R 1 + R R 1 R ) Voltage is the same across resistors 10

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