2. Lecture 2
Introduction to Electronics 2
Resistor Networks
Resistors can be combined in a network to create new resistor values. They
can either be connected in Series or in Parallel.
Series
To find the equivalent resistance of resistors end to end simply add the
resistances:
R1
Rseries
R2 (is equivalent to)
Find the resistance of circuit that has 1kΩ, 4.7kΩ and 22kΩ
resistors in series.
Lecture 2: Introduction to Electronics 2
BTC108: Electronics – James Uren
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3. Parallel
When resistors are connected in parallel the inverse of the combined
resistance is found by adding the inverse of the resistances:
R1 R2 Rparallel
(is equivalent to)
Find the resistance of circuit that has three 4.7kΩ and 22kΩ
resistors in parallel.
Lecture 2: Introduction to Electronics 2
BTC108: Electronics – James Uren
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4. Potential Dividers
Resistors drop a voltage across them. This means more than one resistor
connected in series will divide the input voltage.
I
R1
Vin
R2 Vout
Using Ohm’s Law, show that equation for the potential divider in
the circuit above is:
This method for voltage dividing is extremely useful in electronics as it
provides a simple way of converting resistance to voltage.
For example, a rotary control on a piece of equipment is a variable resistor
(potentiometer or ‘pot’), and by using the control as one of the resistors in a
potential divider it is possible for the rest of the circuit to read off the dial value
as a voltage.
The same principle applies for simple sensor circuits, e.g. a thermistor
whose resistance changes with temperature.
Lecture 2: Introduction to Electronics 2
BTC108: Electronics – James Uren
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5. Resistivity
All materials have a resistance, and this property is called the material’s
resistivity. It is calculated in the following way:
Where:
ρ (pronounced ‘ro’) is the resistivity in m Ω
R is the resistance in Ω
A is the area in m2
l is the length in m
Calculate the resistance of a circular piece of copper wire with
diameter 1mm and length 0.2m.
The resistivity of copper is 1.7 x 10-8.
Lecture 2: Introduction to Electronics 2
BTC108: Electronics – James Uren
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6. Power
All electronic devices consume electric power when in operation. This power,
measured in Watts (W) can be calculated using Joule’s Law:
I
+
V R
Where P is the electric power consumed in resistance R in Watts (W).
Electronic devices and components will normally have a power rating.
Ratings of resistors
Joule’s Law and Ohm’s Law can be combined to give two more expressions
for power:
A piece of equipment with a 12V supply has a power rating of
40W. Is a 2A fuse sufficient?
Lecture 2: Introduction to Electronics 2
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7. Practical: Potential Dividers and Power
Read the Health and Safety Information on page 9.
• Using only 4 identical resistors (of between 1kΩ and 100kΩ) and a 5V
supply, design a potential divider that provides outputs of 2V and 3V.
• Build the circuit and use a voltmeter to show that the voltage outputs
are what you expect.
• Calculate the current in your circuit and use an ammeter to confirm
your answer.
• The resistors are all rated at 0.25W. What power is being consumed in
each resistor?
• What is the lowest resistance you could use for all the resistors in your
circuit to keep under the rating?
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8. Writing Numerical Answers
Decimal Places
Giving an answer to 3 decimal places means three digits after the decimal
point. If the 4th decimal place is 5 or above, round up the 3rd decimal place.
e.g. 65.342545 given to 3 DPs is 65.343
Significant Figures
Giving an answer to 3 significant figures means showing only the 3 left-most
digits (rounding in the same way.
e.g. 65.342545 given to 3 SFs is 65.3
768593.25 given to 3 SFs is 769000
3 significant figures is normally enough information in electronics. Give all
answers to this accuracy unless directed otherwise.
Units
For large and small numbers it is convenient to use an exponential notation
with 10 - ‘to the power’ - X.
e.g. 768593.25 expressed in this way and to 3 SFs is 7.69 x 105
For the following cases this is simplified:
p pico x10-12
n nano x10-9
μ micro x10-6
m milli x10-3
k kilo x103
M mega x106
G giga x109
T tera x1012
e.g. 768593.25 can be expressed (to 3 SFs) as 769 k or 0.769 M.
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10. Health & Safety Considerations
Soldering and de-soldering:
Solder melts at between 180 and 200°C. Soldering irons will heat up to
between 250 and 400°C. Be extremely careful when soldering and take the
following precautions:
• Switch off the soldering iron at the mains when not in use
• Always keep the iron in its stand
• Make sure your workspace is clear, well lit and well ventilated
• Never solder while your circuit is powered up
• Never solder without tutor supervision
• Only apply the soldering iron for the minimum amount of time
• Keep your soldering tidy and use the minimum amount of solder
• Avoid breathing in solder fumes
• You must only use the lead-free solder provided
• You must use tools e.g. pliers to support components that are
being soldered and ensure the board is secure.
Switching it on:
Powering up a circuit that is incorrectly connected can cause components or
equipment to get extremely hot or even ‘blow’. A short circuit (where
unintended electrical connections are made) for example may damage
equipment or blow components causing them to behave in an unpredictable
way.
• Before powering up your circuit you MUST have it checked by the
tutor
• Have your neighbour physically inspect your work before
powering on
• If your circuit does not behave as you expect, switch it off
immediately
• Use your nose! A faulty circuit with hot components will often
smell or smoke
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11. If your circuit does not behave as you expect:
• With the power off, confirm by eye that your circuit is connected
correctly and that you are using all the correct components and
mounted with the correct polarities
• Inspect your circuit closely for short circuits, soldering faults and
dry joints:
• Do all the testing on your circuit that you can with it powered off.
• Be extremely careful when probing your circuit live as the probe
itself can cause short circuits
• When probing with an oscilloscope ensure the earth connection is
applied safely
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