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MIT 8 02X - Voltage, Current and Resistance

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Voltage, Current and Resistance Electric Charge There are two types of observed electric charge, positive and negative. Positive and negative are arbitrary names derived from Ben Franklin’s experiments. He rubbed a glass rod with silk and called the charges on the glass rod positive. He rubbed sealing wax with fur and called the charge on the sealing wax negative. Like charges repel and opposite charges attract each other. The unit of charge, Q , is called the coulomb [C ]. Charge of ordinary objects is quantized in integral multiples Q =+ Ne or Q =−Ne where e =1.6×10−19 C , and N is some positive integer. The electron carries one unit of negative charge, qelectron =−e , and the proton carries one unit of positive charge, qproto n =+e . Voltage Sources Batteries, generators, power supplies are devices that convert some other form of energy into electrical energy. When the terminals of a battery are connected to a wire, forces act on charges, and produce a flow of charge in the wire, an electric current. Here the electrical energy comes from chemical reactions inside the battery. There are many sources of electromotive force: solar cells, generators, and alternators are a few examples. Voltage Difference The voltage difference ∆V ≡VB −VA between points A and B is defined to be the negative of the work done ∆W per charge, q, in moving the charge, q , from any point A to any point B ∆W∆V =−. q Voltage difference is also called electric potential difference. The unit of voltage difference is the volt [V ]. [V ]=[volt ]=[ joule / coulomb] =[J / C]. The work done ∆W in the definition of the voltage difference is the work done by the electric force Br ∆W =∫ F⋅dr r A 1Work-Energy A positive charge free to move will go from a higher potential to a lower potential. Notice that ∆V is negative and q > 0, hence the work done by the electromotive force is positive, (∆W =−q∆V > 0 ). This positive work can be converted to mechanical energy in the form of increased kinetic energy, (∆W =∆K ), or converted to heat, (∆W =∆Qheat ). A negative charge free to move will go from a lower potential to a higher potential. Current Electric currents are flows of electric charge. The electric current through a wire is defined to be the total net charge flowing across any cross-sectional area of the wire per second. The unit of current is the amp [ A] with 1 amp = 1 coulomb/sec. Common currents range from mega-amperes in lightning to nanoamperes in your nerves. There are two different systems of units, the SI or Système International d’Unités, and the CGS (centimeter, grams, sec). In CGS units, charge is a fundamental quantity. The unit for charge is the electrostatic unit [esu ]. In the SI system, current is the fundamental quantity, and electric charge is a derived unit. This means that one coulomb is defined as follows. If one amp of current is flowing through a wire, then the total charge that moves across any cross-section of the wire in one second is defined to be one coulomb of charge. The idea that current, I , is the rate of change of charge, Q , in time can be described mathematically by the relation I =.dQ dt Since flow has a direction, we have implicitly introduced a convention that the direction of current corresponds to the direction positive charges are flowing. Inside wires the flowing charges are negatively charged electrons. So the electrons are flowing opposite to the direction of positive current. There are many kinds of electric current: direct or alternating, high or low frequency, steady or transient, constant, slowly varying, pulsating or fluctuating. Electric currents flow in conductors: solids (metals, semiconductors), liquids (electrolytes) and ionized gases. Electric currents don’t flow (much) in non-conductors or insulators. Power Supplies The rate of doing work is called power. A voltage source ∆V that produces a current I has a power output P =∆VI . Voltage sources are commonly referred to as power supplies. The unit of power is the watt, [W ]; [W ]=[watt] =[volt][amp]=[V ][A]. 2Since power is the rate of change of energy with time, the units of watts are also [W ]=[watt] =[ joule / sec]=[J / s]. Electric Circuits Electrical circuits connect power supplies to `loads’ such as resistors, motors, heaters, or lamps. The connection between the supply and the load is made with insulating wires that are often called `leads’ and soldering, or with many kinds of connectors and terminals. Energy is delivered from the source to the user on demand at the flick of a switch. Sometimes many circuit elements are connected to the same lead, which is the called a `common lead’ for those elements. Various parts of circuits, called circuit elements, can be in series or in parallel, or series-parallel. Elements are in parallel when they are connected `across’ the same voltage difference (see Figure 1). Figure 1: parallel elements Generally, loads are connected in parallel across the power supply. When the elements are connected one after another, so that the current passes through each element without any branches, the elements are in series (see Figure 2). Figure 2: series elements There are pictorial diagrams that show wires and components roughly as they appear, and schematic diagrams that use conventional symbols, somewhat analogous to road maps. 3Often there is a switch in series; when the switch is open the load is disconnected; when the switch is closed, the load is connected. One can have closed circuits, through which current flows, or open circuits in which there are no currents. Sometimes, usually by accident, wires may touch, causing a short circuit. Most of the current flows through the short, while very little will flow through the load. This may burn out a piece of electrical equipment like a transformer. To prevent damage, a fuse or circuit breaker is put in series. When there is a short the fuse blows, or the breaker opens. In electrical circuits, a point (or some common lead) is chosen as the ‘ground’. This point is assigned an arbitrary voltage, usually zero, and the voltage V at any point in the circuit is defined as the voltage difference between that point and ground. Resistance and Ohm’s Law When a voltage difference, ∆V , is applied to a circuit element, a current flows through it. The amount of the current is a function of the voltage. The current-versus-voltage relationship (


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