Resistors Ohm’s Law and Combinations of Resistors See Chapters 1 & 2 in Electronics: The Easy Way (Miller & Miller)
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.
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.
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.
Ammeter in EWB Ammeters are connected in series.
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- e- I e-
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.
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.
Voltmeter in EWB Voltmeters are connected in parallel.
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.
Resistance • The ratio of voltage to current is known as resistance • 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.
Multi-meter being used as ohmmeter in EWB A resistor or combination of resistors is removed from a circuit before using an ohmmeter.
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
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.
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 V
V = I R =
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.”
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
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 = I R • 120 V = I (240 ) • I = 0.5 V/ = 0.5 A
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.
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 b R1 R2 I2 I1
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
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.
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.
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
Equivalent resistance (parallel) • I = I1 + I2 V’s are same, so they cancel
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.
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.
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
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.
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.
Ohmmeter measuring resistance of 1-k and 2 -k resistors in series
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).
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.
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.