Ohm’s Law and Combinations of resistors

Electric Charge Electric charge is a fundamental property of some of the particles that make up matter, especially (but not only) electrons and protons It 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

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

Current Convention Current has a direction By convention the direction of the current is the direction in which positive charge flows If negative charges are flowing (which is often the case), the current’s direction is opposite to the particle’s direction 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

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 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 R = V I

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

Ohmic Ohm’s law is an empirical observation Meaning 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 no where 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 takes 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 Vab = V1 + V2 Req R1 R2 V’s are same, so they cancel 1 = + Req R1 R2

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

Series/Parallel Recap 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

Multimeter A multimeter 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

Voltmeter in parallel with 1-k Resistor

Ammeter in series with 1-k Resistor

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 multimeter 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 One of the differences between Baby AT and ATX cases is in the fan