Resistors
Ohm’s Law and Combinations of
Resistors
See Chapters 1 & 2 in
Electronics: The Easy Way
(Miller & Miller)
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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.
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ESD
 A small amount of charge can build up on one’s
body – you especially notice 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.
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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.
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Ammeter in EWB
Ammeters are connected in series. Think of the charge as starting
at the side of the battery with the long end and heading toward the
side with the short end. If all of the charges passing through the
first object (the resistor above ) must also pass through second
object (the ammeter above), then the two objects are said to be in
series.
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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.
(Blame Benjamin Franklin.)
Current moving to right
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Negative charges moving to left
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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.
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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. If the “tops” of two
objects are connected by wire and only wire and the
same can be said for the “bottoms” , then the two
objects are said to be 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.
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Multi-meter being used as
ohmmeter in EWB
A resistor or combination of resistors is removed from
a circuit before using an ohmmeter.
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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
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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.
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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.
Then, resistance is independent of voltage or
current
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Slope=I/V=1/R
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.”
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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
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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.
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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
a
R1
I1 
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V2
R2
b
I2 
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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
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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.
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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.
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Resistors in parallel
 The voltage across the resistors is the same

V1 = V2 = Vab
 The current is split between the resistors

I = I 1 + I2
R1
R2
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Equivalent resistance (parallel)
 I = I1 + I 2
Vab
Req
1
Req
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=
=
V1
R1
1
R1
+
+
V2
R2
V’s are
same, so
they cancel
1
R2
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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.
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Equivalent Resistance
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1
Req
=
1
R1
+
1
R2
If R1 = 2.3 and R2 = 3.4, then do the following on th
calculator: 2.3 → 1/x → + → 3.4 → 1/x → = → 1/x →
1.37
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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.
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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
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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.
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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.
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Voltmeter in parallel with 1-k
Resistor
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Ammeter in series with 1-k
Resistor
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Ohmmeter measuring resistance of
1-k and 2 -k resistors in series
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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).
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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.
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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.
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