| Resistors,
Volt and Current
By Ibrahim Kamal
Last update:
4/4/08
 Overview
In this article we will study the most basic component in
electronics, the resistor and its interaction with the voltage
difference across it and the electric current passing through
it.
You will learn how to analyse simple resistor networks using
nodal analysis rules
This article also shows how special resistors can be used
as light and temperature sensors. |
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Imagine
the electricity
As a beginner, it is important to be able to imagine the flow
of electricity. Even if you've been told lots and lots of times
how electricity is composed of electrons traveling across a conductor,
it is still very difficult to clearly imagine the flow of electricity
and how it is affected by Volt and resistors. This is why I am
proposing this simple analogy with a hydraulic system, which anybody
can easily imagine and understand, without pulling out complicated
fluid dynamics equations.
Fig. 1: Electrical and
Hydraulic system analogy |
Notice how the flow of electricity
resembles the flow of water from a point of high potential energy
(high voltage) to a point of low potential energy (low voltage).
In this simple analogy water is compared to electrical current,
the voltage Difference is compared to the head difference between
tow water reservoirs, and finally the valve resisting the flow
of water is compared to the resistor limiting the flow of current.
From this analogy you can deduce some rules that you should keep
in mind during all your electronics work:
 Electric current
through a single branch is constant at any point (exactly as you
cannot have different flow rates in the same pipe; what's getting
out of the pipe must equal what's getting in)
There wont be any
flow of current between 2 points if there is no potential difference
between them. In other words, for a flow of current to exist,
there must be a voltage difference between tow points.
The quantity of
water in the reservoir can be compared to the electric charge
stored in a battery. When the level of water in the tow tanks
become the same, there is no more flow of water, and comparatively,
a battery is empty and cannot deliver anymore current when the
tow electrodes have the same voltage.
The electric current
in a conductor will increase with the decrease of the resistance,
exactly as the rate of flow of water will increase with the decrease
of the resistance of the valve.
I could write a lot more deductions based on this simple analogy,
but we can summarize those rules in the most fundamental equations
of electronics: Ohm's law, that you shall learn
in the rest of this article.
The
resistor
The resistor
can be defined by it's main purpose, a device to control
or limit the flow of current, hence we can say that
the main parameter of a resistor is it's resistance, which
is measured in Ohm's ( ).
Never less, another design consideration when working
with resistors is its rated power,
measured in watts (W), which is the quantity of power
the resistor can dissipate without burning out.
It is also important to note that resistors are not only
used for current limiting, they can also be used as voltage
dividers to generate very precise voltages out of bigger
voltages. Some sensors are based on a resistance that
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Fig.2: 1 Watt 880 Ohm resistors
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varies depending on light, temperature or shear
stress, like the LDRs (light dependent resistors),
Thermistors (temperature dependent resistors)
or strain gauges. For more information and pictures, see special
resistors at the end of the article.
Ohm's
law
It's clear that those 3 equations at the right are different
variations of Ohm's law, but the 3 of them must be very
clear in your mind in order to proceed to more complicated
circuits. You have to be able to understand and imagine
the meaning of the equation 2 for example,
which implies that a rise of voltage with a constant resistance
will cause a rise of current. However, it wouldn't be logically
true to say that a current rise will cause a voltage rise
if the resistance is constant (even though this is mathematically
true) because it's the voltage, the potential difference,
that will create a flow of current, not the opposite (refer
to the analogy of the 2 water tanks). Also, equation 3
can be used to deduce the value of the resistance to used
to limit the flow of current to a certain value under a
constant known voltage difference.
Those are just examples showing you the importance of this
rule. You will learn how to use them along the rest of the
article Even the most |
Fig.
3: Ohm's
law.
R: Resistance (ohm)
V: Volts (V)
I: current (I) |
sophisticated electronic simulations software uses
this equation, along with some other equations to solve and simulate
the most complicated circuits.
Series
and parallel resistors
Understanding what is the effect of connecting resistors
in series or in parallel is very important and will help you to
analyze and simplify an electronic circuit, using those simple mathematical
relations for series and parallel resistors:
Fig. 4A |
In this example circuit (figure 4A), R1 and R2 are connected
in parallel, a single resistor R3 can provide the exact same
function of the tow resistors R1 and R2, according to the
law:
Which, in case of only 2 parallel resistors, can be written
as:
Not only this relation can be used to
simplify complicated circuits, but it can also be used to
create resistors of values that you don't have. |
Notice also that the value of R3 will always be smaller than the
2 other equivalent resistors. Which is logic, because adding more
resistors in parallel provides additional paths to the electrical
current, decreasing the overall resistance of the circuit.
Fig. 4B |
Series resistors can also be grouped together and replaced
by one resistor, whose value would equal the summation of
the tow initial resistors, which is again very logical, due
to the fact that this configuration of resistance will provide
additional resistance to the flow of current. Therefore the
equivalent resistor R3 can be very simply calculated by the
relation:
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Fig. 4C |
At last, be careful of this very common pitfall among beginners,
which is shown in figure 4C.
It must be very clear that for 2 resistors to be considered
as series resistors, they must be share the same current,
as you will see in the rest of the tutorial. |
Resistor
used for current limiting
The most basic role of resistors is current limiting, which consist
of precisely controlling the quantity of electrical current that
is going to flow through a device or a conductor. To
understand
how current limiting resistors work, let's first study this
simple schematic (figure 5A), where a lamp is directly connected
to a 9V battery. A lamp, like any other device that consumes
electricity to accomplish a certain task (like providing
light in this example) has an internal resistance, that
determines how much current it will consume. So, from now
on, any resistive device can be replaced in by a resistance
especially in electronics schematics. (you can also notice
in Figure 5B -which is equivalent to the 9V battery
and |
Fig.5A
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the
lamp- the symbol of a resistor in the schematics, and
how it is connected to the the Positive and negative power
sources).
Now if the lamp is to be considered a resistor, we can then
use Ohm's law to calculate the current passing through it.
Ohm's law states that the current passing through a resistor
is equal the the voltage difference across it divided by
the resistance of that |
Fig. 5B
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resistor. This is mathematically
written as:
 ,
or more accurately as:
 .
Where ( )
is the voltage difference across the resistor and (R)
is the resistance of the resistor (it's value)
Now notice the Figure 5C, where a current limiting resistor
have been added. This resistance will limit the current
going to the lamp, simply as it's name implies. You can
control, to a very precise extent, the amount of current
flowing through the lamp simply by choosing the right value
for the resistor R1. A large resistor will highly reduce
the current while a small resistor will allow more current
(exactly as in our hydraulic analogy, where the valve is
compared to |
Fig. 5C |
a resistor). Mathematically
speaking, this can be written as:
 .
It is then clear that the value of the current will decrease if
the value of the resistor R1 increases. Hence a resistor
can be used to limit the current.
However it is important to note that this comes
with a cost, which is the heat dissipated into the current limiting
resistor, and you must chose a resistor of a suitable power rating,
as you will see in the rest of the tutorial.
Resistors
used as Voltage
divider
 Fig.
6A
 Fig.
6B |
As the name implies, resistors can also be used as voltage
divider, in other words they can be used to generate any
voltage from an initial bigger
voltage by dividing it. The mathematical relation for
this resistor configuration shown in figure 6A (that you
could easily prove using the nodal analysis
method) is:
...(Equ. 6A)
In case both resistors have the same value ( ),
the equation can be written as:
Another common special case of this resistor configuration,
is when the lower resistor is connected to ground (0V)
as shown in figure 6B.
Replacing Vb by 0 in the equation 6A,
we get:
...(Equ. 6B)
Which is the most common voltage divider equation. |
You could imagine a lot more of special cases for
this resistor configuration, and you shall discover them as you
are working your way into the field of electronics.
Nodal
analysis
Now that you're beginning to deal with electronic schematics,
it is important to be able to analyze them and calculate any required
voltage, current or resistance. There are many ways to study an
electronic circuit, one of the most common methods is the Nodal
analysis, where you simply apply a set of rules
on a circuit of any size and calculate step by step all the required
variables.
Simplified nodal analysis rules:
Fig.
7A |
Definition of a node
A node is any point in the circuit. Points that
are connected to each others by wires, without any
other component between them are considered as a
single node. Therefore, the infinite number of point
in a wire are considered as only one node.
All points that are grouped as a single node have
the same voltage. |
Fig.
7B |
Definition of a branch
A branch is a set of 1 or more components connected
in series, and all the components that are connected
in series in the same chain are considered as 1
branch
The
current flowing along a branch is the same at all
points.
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Fig.
7C
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All nodes voltages are relative to a fixed reference
node, usually the ground connection whose symbol
is ( )
and whose voltage is always equal 0 Volts.
Current always flows from a node
to another node of lower voltage.
The
voltage of a node can be determined from the voltage
of a nearby node, Using the relation:
 ,
and rearranging we get:
 ,
where V2
is the voltage of the node to be determined, V1
is the voltage of the reference node which is known,
I1 is the current flowing from
node 1 to node 2
And R1 is the equivalent resistance
between the 2 nodes.
Similarly, and still using the same Ohm's law, the
current in a branches can be determined if the voltages
at the 2 nodes at both ends of the branches are
known, using the relation:
Current entering the node equals current leaving
the node, thus in the given example (figure 7C)
this can be written as :
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It is important to be able able to feel the meaning of
those simple mathematical relations; For example in the
figure 7C above, the current is flowing from V1 to V2,
and thus V2 must be smaller than V1 and that's exactly
what the relation:
is proving.
The idea is to dig your way around the circuit to be analyzed
with those given rules. Using the appropriate rule at
the appropriate time, is the key to a fast and easy circuit
analysis and understanding, and this skill is gained by
practice and experience. Finally, remember that computers
can do it, and so do you.
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Calculating
required rated power of a resistor
When buying resistor to build a certain circuit, you may be asked:
"what is the power rating of the resistors you want to buy?"
or you may simply be given 1/4 Watt resistor as they are the most
standard class of resistors.
As long as you're working with resistor of higher value than 220,
and your power supply delivers 9V or less, it is safe to work
with 1/8 watt or 1/4 watt rated resistors. But if the voltage
across a resistor increases over 10V or the resistor's value is
less than 220,
you should calculate the power carried away by the resistor, otherwise,
it may burn up in fumes and can even cause serious burns and injuries.
To calculate the required power rating of the resistor, you must
first know the voltage difference across the resistor (V) and
the current flowing through it (I), then the power (P) is:
where I is the electrical current in Amperes (A), V is the voltage
in Volts (V) and P is the power dissipation in Watt (W)
Here you can see some resistors having different power ratings.
you notice that the main difference between different power ratings
is the size of the resistor.
Fig. 9 |
Special
resistors
Resistors can get more sophisticated than this, from simple variable
resistors (also called potentiometers), to highly accurate temperature,
light, and pressure sensors. Some of them are going to be discussed
in this section.
Variable
resistor (Potentiometer)
Fig. 10A
Fig. 10B
Fig. 10C
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Figure
10A shows the schematic symbol of a variable resistor.
It is often referred to as a potentiometer, because it
can be used as a potential (voltage) divider. Figure 10C
shows how potentiometers look like in reality, they vary
in size and shape, but they all work the same way. The
pins at the right and left extremities of the potentiometer
are equivalent to the fixed point (like Va
and Vb in the figure 10A), while the
middle pin is the moving part of the potentiometer, and
is used to change the ratio of the resistance at its left
to the resistance at its right. hence the voltage
divider equation applies to the potentiometer, which
can deliver any voltage from Va to Vb.
Also a variable resistor can be used in a current limiting
configuration by connecting the output the point Vout
to Vb like in the figure 10B. Imagine how the current
will flow through the resistance from the left extremity
to the right until it reaches the arrow (the moving part
that varies resistance) then practically all current will
flow through the jumper wire (theoretically some very
little current will pass through the rest of the resistor)
This way you can also use a potentiometer to adjust the
current flowing into any electronic component, or lamp
for example. Actually this is how most of the old light
dimmers work.
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LDR (Light Dependent Resistors) and thermistors
There many electronic sensors that rely on a resistor whose resistance
varies with respect to another parameter like light, temperature,
or pressure. We are going to briefly study LDRs (Light Dependent
Resistors) and Thermistors (Temperature dependent resisters),
and you will notice that all resistors based sensors work exactly
the same way, as the the easiest way to use one of those sensors
is to put them in a voltage divider configuration, obtaining a
voltage that changes with the measured values, instead of a resistance
change. Sensors whose output is Voltage variations are much easier
to interface to computers or microcontrollers, as you shall see
during the next tutorials.
Fig.
11A |
As you can see in figure 11A, LDRs vary in size, but they are
all resistors whose resistance will decrease when exposed to light,
and increase when shed in the dark. they are also referred to
as photoresistors, photoconductors
or Cds because they are made of Cadmium sulphide
Unfortunately, LDRs response can be slow, and they also often
tend to lack accuracy, but still,
Fig. 11B
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they are very easy to use (see example here).
For applications that requires more accuracy, and faster
response, photodiodes or phototransistors are preferred
over LDRs. Usually, an LDR's resistance can vary from
50
in the sun light, to over 10M
in absolute darkness. As we said before, The variation
of resistance has be converted into a voltage variation,
by introducing the LDR into a voltage divider configuration,
as shown in figure 11B.
Recalling equation 6B, you will
see that the output voltage (Vout) of this circuit follows
the following equation:
Supposing that the LDR's resistance varies from 10M
to 50,
calculations would yield that Vout varies
respectively from 0.005V to 4.975V. This voltage variation
can be then fed to an integrated circuit named an Operational
Amplifier to create a reliable light sensor. |
Similarly, a Thermistor can be used in the exact same way to create
a sensor whose voltage varies with temperature variation. However,
thermistors comes in much more varieties and types than LDRs,
for instance, A thermistor can either be a negative temperature
coefficient type (NTC) whose resistance will decrease with temperature
rise, or positive temperature coefficient type(PTC), whose resistance
will increase with temperature rise. Nowadays, electronics manufacturers
provide thermistors of very high quality in terms of accuracy
and response time, inneed, it's very common to see thermistors
in very precise devices like digital thermostats.
Schematic
Symbols
Figure 12 shows the most common symbols for the various types
of resistors, which are used when drawing electronic schematics.
Fig.
12
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Resistors
color code
There are tow common ways to know a the value of a resistor,
by measuring it using an Ohmmeter, or by reading the color code
printed on it, which is much faster, when you get used
Fig. 13A
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to
it. As you can see in figure 13A, some
resistors have 4 color bands on it, and some have 5. Both
of them use the same encoding method. the bands named
1, 2 or 3 in figure 13 can be translated into a 2 or 3
digit number using the table below. the band named M is
the multiplier, meaning the number obtained from the previous
digits have to be multiplied by 10 to the power M (or
simply, add M number of zeros after the 2 or 3 digits
number). the Value of M is |
Also obtained from the table below. The last band
at the right (T) is the tolerance band, which is usually gold
meaning 5% tolerance or silver meaning 10%.
Black |
Brown |
Red |
Orange |
Yellow |
Green |
Blue |
Violet
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Gray |
White |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
Table
used for translating color bands to numbers |
To read a resistor using the color encoding
follow the same steps of this example. Let's say you have a resistor
like the one shown in figure 13B, the first step is to locate
the tolerance band,
Fig. 13B
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it is usually
apart from the other bands, and it is typically gold or
silver colored. Once the tolerance band is located, note
the colors of the bands starting from the other side. The
first 2 bands will be translated from the table to become
a '1' and a '0', this will |
be considered as 10,
then the Multiplied band, being red, will mean that you multiply
by 10 the the power 2, or simply, multiply by
100. the the first 2 digits (10) multiplied by (100) will yield
a result of 1000. Then, this is a 1000
resistor, or 1K.
Preview of the last 15
messages discussing this page. Messages are sorted from the newest to
the oldest. |
Posted
by:
tigermoth
on:
01 Aug 2008 |
Re: Resistors, Volt and Current |
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Hi , I am new at this, and trying to sort a damaged resistor on a circuit. it seems colour coded black,white,white, orange, which should not be, it takes 120v down to sense power on to control a relay on a 12v powered controller for a gas/electric fridge, which has been converted to run on 240v. hence it has overheated and burned out. Any ideas? Thanks, John.
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Posted
by:
solar
on:
19 Jul 2008 |
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Posted
by:
ikalogic
on:
19 Jul 2008 |
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Re: Resistors, Volt and Current |
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Quoting solar: haha... you should really consider being a reseller.
I live in Edmonton, Alberta, (Canada). I was thinking of buying it online but if you happen to know somewhere that sells that specific part in my area:-) |
Well, i know there are many electronics stores that are based on canada but also accept orders by internet, i this this is your best bet.
I do the same in France, i always order from conrad.fr, and i receive the articles in 48 hours.
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Posted
by:
solar
on:
18 Jul 2008 |
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Re: Resistors, Volt and Current |
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haha... you should really consider being a reseller.
I live in Edmonton, Alberta, (Canada). I was thinking of buying it online but if you happen to know somewhere that sells that specific part in my area:-)
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Posted
by:
ikalogic
on:
18 Jul 2008 |
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Re: Resistors, Volt and Current |
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Quoting solar: Thanks, I'm really enjoying your site.
And thank you so much for tell me what type of component I need, even searching up the exact model and doing all this in record time! I agree that the KA7815 is probably the best model to get. Do you have a recommended place where I can buy this component? Do you sell components?
Cheers! |
I which i sold components, i would be less poor  (just joking)
Where do live? or you're going to buy from internet?
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Posted
by:
solar
on:
18 Jul 2008 |
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Re: Resistors, Volt and Current |
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Thanks, I'm really enjoying your site.
And thank you so much for tell me what type of component I need, even searching up the exact model and doing all this in record time! I agree that the KA7815 is probably the best model to get. Do you have a recommended place where I can buy this component? Do you sell components?
Cheers!
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Posted
by:
ikalogic
on:
18 Jul 2008 |
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Re: Resistors, Volt and Current |
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Hello and welcome to ikalogic.
You need a very simple circuit called a voltage regulator.
The most simple type are the linear regulators, and the most adequate one to your application seems to be the 7815, which provides a clean 15V output from any DC voltage ranging from 19 to 35 volts.
I uploaded a datasheet of that component.
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Posted
by:
solar
on:
18 Jul 2008 |
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Resistors, Volt and Current |
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Thank you for your fascinating tutorial. I still have a specific question I have been struggling with and would like to ask for your advice:
I'm trying to set up a solar charging system for a 12 Volt car battery. My problem is that the solar panel which I purchased to charge the battery produces 21V DC at 0.5A. Apparently car batteries should be charged at 13 to 15 Volts. So I assume that due to the high wattage (according my calculations: 21*0.5=10.5W), a voltage divider with resistors wouldn't help me. Would you have a recommendation as to how I might reduce the 21 Volt supply to 15 Volts?
Thanks!
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Posted
by:
ikalogic
on:
04 May 2008 |
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Re: Resistors, Volt and Current |
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| Quoting msgt81: I have been looking and can't find what I'm after and don't know if it even exists. I'm looking for a chart or some way to determine what ohm resister to use in different apps. The problem I have at the present is; reduce 5.5 VDC, so I can power a LED that draws 35mA @ 3.2 (typical) 3.5 (max)VDC. Is there such a chart available? or HELP!! |
I don't think there is.. at least i've never seen one.. but stick to the calculations provided in this tutorial, it will be come more intuitive as you use them a lot...
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Posted
by:
msgt81
on:
03 May 2008 |
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Re: Resistors, Volt and Current |
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I have been looking and can't find what I'm after and don't know if it even exists. I'm looking for a chart or some way to determine what ohm resister to use in different apps. The problem I have at the present is; reduce 5.5 VDC, so I can power a LED that draws 35mA @ 3.2 (typical) 3.5 (max)VDC. Is there such a chart available? or HELP!!
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Posted
by:
ivory
on:
01 Apr 2008 |
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Posted
by:
ikalogic
on:
31 Mar 2008 |
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Re: Resistors, Volt and Current |
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| Quoting ivory: To discharge a capacitor, the capacitor can be connected to a resistor. |
I do not agree with that, The higher the resistance, the slower the capacitor will be discharged. That's because the high resistor will limit the current, so it will take more time to for the capacitor to be discharged.
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Posted
by:
ivory
on:
30 Mar 2008 |
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Re: Resistors, Volt and Current |
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To discharge a capacitor, the capacitor can be connected to a resistor. The higher the resistance, the faster the capacitor will be discharged.
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Posted
by:
truthbydenial
on:
28 Mar 2008 |
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Re: Resistors, Volt and Current |
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What I understand about using a resistor with a capacitor is: you may wish to delay the time that it takes for a capacitor to charge. Using a resistor would make a capacitor take a longer time to fully charge and would protect the capacitor in a circuit where the voltage may be otherwise too much for the capacitor by itself to handle. It is possible to blow a capacitor, so adding a resistor into the circuit may help to prevent just that.
A pot, or potentiometer, is a variable resistor. What is nice about it is you are able to control the amount of resistance by turning a dial. You can pick up a handful of these for cheap from radio-shack, or any device with a volume nob. Testing the effects of a resistor with a capacitor in a simple circuit using a multimeter would be fun, and more efficient using a potentiometer instead of a fixed resistor.
Let me know if you find anything else on relationships between resistors and capacitors! Oh, and thanks for the post. I thought it was just me here, lol.
I am a little confused on the method of discharging a capacitor once it has fully charged. If you have any information on methods used to discharge capacitors, I would like you to share that.
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Posted
by:
ivory
on:
28 Mar 2008 |
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Re: Resistors, Volt and Current |
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Hello, thanks so much for the tutorial.
May i ask a question on "charging a capacitor with resistor"?
What is the use or effect of the resistor in the process of charging a capacitor?
Can i charge a capacitor without resistor? I mean i just connect an uncharged capacitor to a battery, without any resistor connected in series.
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