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Resistors Ohm’s Law and Combinations of Resistors See Chapters 1 & 2 in Electronics: The Easy Way (Miller & Miller) PHY 202 (Blum) 1 Electric Charge Electric charge is a fundamental property of some of the particles that make up matter, especially (but not only) electrons and protons. Charge comes in two varieties: Positive (protons have positive charge) Negative (electrons have negative charge) Charge is measured in units called Coulombs. A Coulomb is a rather large amount of charge. A proton has a charge 1.602 10-19 C. PHY 202 (Blum) 2 ESD A small amount of charge can build up on one’s body – you especially notices it on winter days in carpeted rooms when it’s easy to build a charge and get or give a shock. A shock is an example of electrostatic discharge (ESD) – the rapid movement of charge from a place where it was stored. One must be careful of ESD when repairing a computer since ESD can damage electronic components. PHY 202 (Blum) 3 Current If charges are moving, there is a current. Current is rate of charge flowing by, that is, the amount of charge going by a point each second. It is measured in units called amperes (amps) which are Coulombs per second (A=C/s) The currents in computers are usually measured in milliamps (1 mA = 0.001 A). Currents are measured by ammeters. PHY 202 (Blum) 4 Ammeter in EWB Ammeters are connected in series. PHY 202 (Blum) 5 Current Convention Current has a direction. By convention the direction of the current is the direction in which positive charge flows. The book is a little unconventional on this point. If negative charges are flowing (which is often the case), the current’s direction is opposite to the particle’s direction Current moving to right Negative charges moving to left e- I e- e- PHY 202 (Blum) 6 Potential Energy and Work Potential energy is the ability to due work, such as lifting a weight. Certain arrangements of charges, like that in a battery, have potential energy. What’s important is the difference in potential energy between one arrangement and another. Energy is measured in units called Joules. PHY 202 (Blum) 7 Voltage With charge arrangements, the bigger the charges, the greater the energy. It is convenient to define the potential energy per charge, known as the electric potential (or just potential). The potential difference (a.k.a. the voltage) is the difference in potential energy per charge between two charge arrangements Comes in volts (Joules per Coulomb, V=J/C). Measured by a voltmeter. PHY 202 (Blum) 8 Volt = Joule / Coulomb = PHY 202 (Blum) 9 Voltmeter in EWB Voltmeters are connected in parallel. PHY 202 (Blum) 10 Voltage and Current When a potential difference (voltage) such as that supplied by a battery is placed across a device, a common result is for a current to start flowing through the device. PHY 202 (Blum) 11 Resistance The ratio of voltage to current is known as resistance R = V I The resistance indicates whether it takes a lot of work (high resistance) or a little bit of work (low resistance) to move charges. Comes in ohms (). Measured by ohmmeter. PHY 202 (Blum) 12 Multi-meter being used as ohmmeter in EWB A resistor or combination of resistors is removed from a circuit before using an ohmmeter. PHY 202 (Blum) 13 Conductors and Insulators It is easy to produce a current in a material with low resistance; such materials are called conductors. E.g. copper, gold, silver It is difficult to produce a current in a material with high resistance; such materials are called insulators. E.g. glass, rubber, plastic PHY 202 (Blum) 14 Semiconductor A semiconductor is a substance having a resistivity that falls between that of conductors and that of insulators. E.g. silicon, germanium A process called doping can make them more like conductors or more like insulators This control plays a role in making diodes, transistors, etc. PHY 202 (Blum) 15 Ohm’s Law Ohm’s law says that the current produced by a voltage is directly proportional to that voltage. Doubling the voltage, doubles the current Resistance is independent of voltage or current I Slope=I/V=1/R PHY 202 (Blum) V 16 V=IR = PHY 202 (Blum) 17 Ohmic Ohm’s law is an empirical observation “Empirical” here means that it is something we notice tends to be true, rather than something that must be true. Ohm’s law is not always obeyed. For example, it is not true for diodes or transistors. A device which does obey Ohm’s law is said to “ohmic.” PHY 202 (Blum) 18 Resistor A resistor is an Ohmic device, the sole purpose of which is to provide resistance. By providing resistance, they lower voltage or limit current PHY 202 (Blum) 19 Example A light bulb has a resistance of 240 when lit. How much current will flow through it when it is connected across 120 V, its normal operating voltage? V=IR 120 V = I (240 ) I = 0.5 V/ = 0.5 A PHY 202 (Blum) 20 Series Two resistors are in series if a charge passing through the first resistor must pass through the second resistor. It has nowhere else to go. PHY 202 (Blum) 21 Resistors in series Each resistor obeys Ohm’s law V1 = I1 R1 and V2 = I2 R2 The current through the resistors is the same I1 = I2 = I V1 V2 a R1 R2 b I1 I2 PHY 202 (Blum) 22 Equivalent resistance (series) The equivalent resistance is the value of a single resistor that can take the place of a combination Has same current and voltage drop as combo Vab = V1 + V2 (the voltages add up to the total) Vab = I1R1 + I2R2 Vab = I (R1 + R2) Vab = I Req Req = R1 + R2 PHY 202 (Blum) 23 Resistors in series Resistors in series add. The equivalent resistance is larger than either individual resistance. If there are more things one has to go through, it will be more difficult. PHY 202 (Blum) 24 Equivalent Resistance PHY 202 (Blum) 25 Parallel Two resistors are in parallel if the top ends of the two resistors are connected by wire and only wire and likewise for the bottom ends. A charge will pass through one or the other but not both resistors. PHY 202 (Blum) 26 Resistors in parallel The voltage across the resistors is the same V1 = V2 = Vab The current is split between the resistors I = I1 + I2 R1 R2 PHY 202 (Blum) 27 Equivalent resistance (parallel) I = I1 + I2 Vab V1 V2 = + V’s are Req R1 R2 same, so they cancel 1 1 1 = + Req R1 R2 PHY 202 (Blum) 28 Resistors in parallel Resistors in parallel add reciprocally. The equivalent resistance will be smaller than either individual resistance. It is always easier if one has a choice of what one has to go through. PHY 202 (Blum) 29 Equivalent Resistance PHY 202 (Blum) 30 Fire in a theater analogy If it bothers you that the resistance of two resistors in parallel is lower than either resistor, consider the following. A fire starts in a packed theatre and there is one door through which everyone must exit. It’s a difficult task to get everyone out. A second exit is found, the second exit is narrower and fewer people can use it. However, the theater can be emptied much faster using two exits than one – even if a given person can only use one of the exits. PHY 202 (Blum) 31 Series/Parallel Recap Series Resistors in series have the same current. Their voltages add up to the total voltage. Rs = R1 + R2 Parallel Resistors in parallel have the same voltage. Their currents add up to the total current. 1/Rp = 1/R1 +1/R2 PHY 202 (Blum) 32 Serial and parallel connections A connection is said to be serial if all of the bits entering follow exactly the same path, bits then arrive one-by-one. A connection is said to be parallel if there are a set of paths, bits can then take different paths and groups of bits can arrive simultaneously. PHY 202 (Blum) 33 Multi-meter A multi-meter can serve as a voltmeter, ammeter or ohmmeter depending on its setting. To measure the voltage across a resistor, the voltmeter is placed in parallel with the resistor. To measure the current through a resistor, the ammeter is placed in series with the resistor. To measure the resistance of a resistor, the resistor is removed from the circuit and each end is connected to an end of the ohmmeter. PHY 202 (Blum) 34 Voltmeter in parallel with 1-k Resistor PHY 202 (Blum) 35 Ammeter in series with 1-k Resistor PHY 202 (Blum) 36 Ohmmeter measuring resistance of 1-k and 2 -k resistors in series PHY 202 (Blum) 37 Checking continuity A wire or cable is metal (a conductor) on the inside and thus has a low resistance. A broken cable has a high resistance. To check a cable, remove the cable, set the multi-meter to ohmmeter Check each wire for “continuity” (should find a low resistance). PHY 202 (Blum) 38 Heat A basic principle of physics is that energy is conserved, that is, energy is never lost or gained but only rearranged and put in different forms. When we have a simple resistor circuit, the potential energy that was in the battery becomes heat which is another form of energy. PHY 202 (Blum) 39 Cooling off When you run a computer, heat is constantly being generated because current is passing through circuits that have resistance. Too much heat can damage the circuits. The heat sink and the fan are used to reduce the amount of heat. PHY 202 (Blum) 40