# Resistors s04 by L9k7v8N5

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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-
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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.
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Volt = Joule / Coulomb

=

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Voltmeter in EWB

Voltmeters are connected in parallel.
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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.

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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

=

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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

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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

 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

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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

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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

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