Basic Electronics and Robotics Training Course: Part 2

In this chapter, we will continue learning about resistors and how they are used in the following settings and laws:

  • Resistors in Series
  • Resistors in Parallel
  • How resistors are used
  • Capacitor Basic

Before proceeding, please remember that working with electronics can be dangerous. Make sure to be careful and follow all safety precautions when working on your project.

Also, make sure you read through part 1!

    Before we get started, let’s look at how the resistors are coded with color bands and what it means.

    Print out this chart for your bench for a quick reference when calculating resistor values.

    Try to remember these colors and their color value; this will help you identify the ratings of any standard carbon resistor more quickly.

    If you look at a resistor, you will see 4 bands of color. The first 2 colors are the numeric number for the value and the 3rd is a multiplier of the first 2 numbers and then the 4th color is it's tolerance.  Meaning that the measured value of the resistors ohm will be in-between this percentage.

    2         0           4           5%

    204 = 20 x 10,000 = 200,000 ohm or 200K ohm

    Note:  You see that all I did was added four zeros to the end of the first two numbers--so don’t let the multiplying throw you off.

    Tolerance = 200,000 x .05 = 10,000 +- the total resistance
    So now this resistor can be anywhere between 210K and 190K
    200,000 + 10,000 = 210,000 or 210K ohms
    200,000 – 10,000 = 190,000 or 190K ohms

    The letter K stands for 1,000 ohm so 210K = 210 x 1,000 = 210,000 ohms

    Note:  Most resistors are between 1 to 1 ½% tolerances of the manufacturing noted value, but can be as high or as low as its given tolerance.

    Go ahead and try some other colors on your own to get a better understanding of how the color coding works.

    Resistors in Series

    When you place resistors in series, their ohmic values simply add together to get the total resistance. This is easy to see intuitively, and it’s quite simple to remember.

    Suppose the following resistances are hooked up in series with each other: 112Ω, 470Ω, and 680Ω. What is the total resistance of the series combination?

    Just add the values or each resistor, getting a total of 112 + 470 + 680 =  1262 Ω. You might round this off to R = 1260 Ω. It depends on the tolerances of the components how precise their actual values are to the ones specified by the manufacturer you use.

    Now, it's time to prove what we just learned. You’ll need some resistors of any value and as many as you want to try to calculate in series, A calculator to add the values, a multi-meter and a breadboard.

    These are the resistors that I had just picked out at random in my stock.

    47K = 47,000 Ohms [ Yellow, Purple, Orange, Gold ]
    27K = 27,000 Ohms [ Red, Purple, Orange, Gold ]
    2.2K = 2,200 Ohms [ Red, Red, Red, Gold ]
    1K = 1,000 Ohms [ Brown, Black, Red, Gold ]

    If we put these in serial to each other on the breadboard and take a reading using our meter, then the resistance should be as follows:

    47000 + 27000 + 2200 + 1000 = 77,200 Ohms or 77.2K for short

    Now, let’s make that reading.  My meter reads 75.6K.

    But wait!! You say, “ I thought it was going to be 77.2K Ohms? What happened?”

    Remember that Gold band on the resistors? Well if you remember that it means that there is a 5% tolerance on those resistors, so the reading can be between 5% up or down on the reading of each resistor. So let’s take a look at it in full at a 5% tolerance of our added resistance and see if our reading is in-between these values.

    77,200 * 5% = 77,200 * .05 = 3,860 ohms +-

    77,200 – 3,860 = 73,340 ohms

    77,200 + 3,860 – 81,060 ohms

    So the reading I got from my meter is correct and so the resistors are within the 5% tolerance.

    Do as many of these as you like to make sure you understand how series work with resistors.


    Resistances in Parallel

    When resistors are placed in parallel, they behave differently than they do when they are in series.  So, if you have a resistor of a certain value and you place other resistors in parallel with it, the overall resistance will decrease instead of increasing like with series.  One way to look at resistors in parallel is to consider them as conductances instead. In parallel, conductances add, just as resistors add in series. If you change all the ohmic values to siemens, you can add these figures up and convert the final answer back to ohms.

    The symbol for conductance is G. R is the symbol for resistance in ohms so you use these formulas:

    G = 1/R, and
    R = 1/G

    Consider five resistors in parallel. Call them R1 through R5, and then call the total resistance R.

    So, if R1 = 100Ω, R2 = 200Ω, R3 = 300Ω, R4 = 400Ω and R5 = 500Ω.
    What is the total resistance, R, of this parallel combination?

    Converting the resistances to conductance values, you get
     G1 = 1/100 = 0.01 siemens
     G2 = 1/200 = 0.005 siemens
     G3 = 1/300 = 0.00333 siemens
     G4 = 1/400 = 0.0025 siemens
     G5 = 1/500 = 0.002 siemens

    So adding these gives:
    G = G1 + G2 + G3 + G4 + G5
    G = 0.01 + 0.005 + 0.00333 + 0.0025 + 0.002 = 0.0228 siemens.

    The total resistance is therefore:

    R = 1/G

    R = 1/0.0228 = 43.8Ω

    There is a bit more math involved with finding the resistance in parallel than in series, but now you understand how resistors in parallel work and how each is found. Go ahead and do some more on your own using the figure above and change their resistance so you really understand how this works.

    The Purpose of a Resistor

     Resistors can play any of numerous different roles in electrical and electronic equipment.

    Here are a few of the more common ways resistors are used.

    Voltage Division

    When designing voltage divider networks, the resistance values should be as small as possible, without causing too much current drain on the power supply. The optimum values depend on the nature of the circuit being designed.  The reason for choosing the smallest possible resistances is that, when the divider is used with a circuit, you do not want that circuit to upset the operation of the divider. The voltage divider “fixes” the intermediate voltages best when the resistance values are as small as the current-delivering capability of the power supply will allow.

    This figure below illustrates voltage division.

    The individual resistors are R1, R2, R3, … Rn.

    The total resistance is R = R1 + R2 + R3 +... _ Rn.

    The supply voltage is E

    The current in the circuit is therefore I =  E/R { Remember Ohms Law: E=IR}.

    At the various points P1, P2, P3, … Pn. So at each point the current Iη will differ at each point.

    Voltages will be E1, E2, E3, ..., En. The last voltage, Eη, is the same as the supply voltage, E.

    All the other voltages are less than E, so E1 < E2 < E3 < ... < En = E. (The symbol < means “is less than.”)

    So, let’s do some math to help you out here:

    Let’s say R1 = 100, R2 = 470, R3 = 1,000, R4 = 4700

    R = R1 + R2 + R3 + R4
    R = 100 + 470 + 1,000 + 4,700 =  6,270 ohms

    Let’s say E = 9 volts

    So what is our (current) I
    E = IR
    I = E / R
    I = 9 volts / 6270 ohms
    I = 0.00143 amps or 1.43mA

    Now that we have our total current used in the circuit, we can find out what our voltage is on each of the rest of the resistor points.


    P1 = R1*I
    P1 = 100 * 0.00143
    P1 = 0.143 Volts

    P2 = (R1 + R2) * I
    P2 = (100 + 470) * 0.00143
    P2 = .8151 Volts

    P3 = (R1 + R2 + R3) * 0.00143
    P3 = (100 + 470 + 1000) * 0.0143
    P3 = 2.2451 Volts

    P4 = (R1 + R2 + R3 + R4) * I
    P4 = (100 +470 + 1000 + 4700) * 0.00143
    P4 = 8.9661 Volts

    Note that P4 does not = 9 volts, this is because of rounding off the numbers but if you measured it on the meter it would equal the voltage you are supplying but if we round this number off then it will equal 9 volts.


    Biasing Transistors

    In order to work efficiently, transistors need the right bias. This means that the control electrode—the base, or gate—must have a certain voltage or current. (We will get into this in later chapters with transistors)  Networks of resistors accomplish this. Different bias levels are needed for different types of circuits. A radio transmitting amplifier would usually be biased differently than an oscillator or a low-level receiving amplifier.  Sometimes voltage division is required for biasing like what’s in the figure below. Other times it isn’t necessary. The Figure below shows a transistor whose base is biased using a pair of resistors in a voltage-dividing configuration.

    Current Limiting

    Resistors interfere with the flow of electrons in a circuit. Sometimes this is to prevent damage to a component or circuit. A good example is in a receiving amplifier. A resistor can keep the transistor from using up a lot of power just getting hot. Without resistors to limit or control the current, the transistor might be overstressed and burn out or by carrying direct current that doesn’t contribute to the signal. An improperly designed amplifier might need to have its transistor replaced often, because a resistor wasn’t included in the design where it was needed, or because the resistor isn’t the right size. Remember this when designing an H-Bridge motor controller for your robot.  Below is shown a current-limiting resistor connected in series with a transistor. Usually, it is in the emitter circuit as shown in this diagram, but it can also be in the collector circuit as well.

    Power dissipation

    Dissipating power as heat is not always bad. Sometimes a resistor can be used as a “dummy” component, so that a circuit “sees” the resistor as if it were something more complicated. In radio, for example, a resistor can be used to take the place of an antenna. A transmitter can then be tested in such a way that it doesn’t interfere with signals on the airwaves. The transmitter output heats the resistor, without radiating any signal. But as far as the transmitter “knows,” it’s hooked up to a real antenna as in the diagram below. Another case in which power dissipation is useful is at the input of a power amplifier. Sometimes the circuit driving the amplifier (supplying its input signal) has too much power for the amplifier input. A resistor, or network of resistors, can dissipate this excess so that the power amplifier doesn’t get too much drive.


    Bleeding off Charge

    In a high-voltage, direct-current (DC) power supply, capacitors are used to smooth out the fluctuations in the output. These capacitors acquire an electric charge, and they store it for awhile. In some power supplies, these filter capacitors hold the full output voltage of the supply, say something like 750V, even after the supply has been turned off, and even after it is unplugged from the wall outlet. If you attempt to repair such a power supply, you might get zapped by this voltage. Bleeder resistors, connected across the filter capacitors, drain their stored charge so that servicing the supply is not dangerous.

    It’s always a good idea to short out all filter capacitors, using a screwdriver with an insulated handle, before working on a high-voltage dc power supply. I recall an instance when I was repairing the power supply for a TV unit back in the last 90’s. The capacitors were holding about 2 kV. My supervisor was looking over my shoulder. I said, “Going to be a big pop”, and I took a flat headed screwdriver out, making sure I had hold of the insulated handle only, and shorted the filter capacitor to the chassis. Bang! It melted the tip of my screwdriver. So even if a supply has bleeder resistors, they still take awhile to get rid of the residual charge off the capacitor. For safety, always do what I did, whether your supervisor is around or not to protect you life from electrical shock and burn.


    Two sheets, or strips, of foil can be placed one on top of the other, separated by a thin, non-conducting sheet such as paper, and then the whole assembly can be rolled up to get a large effective surface area. When this is done, the electric flux becomes great enough so that the device exhibits significant capacitance. In fact, two sets of several plates each can be meshed together, with air in between them, and the resulting capacitance will be significant at high ac frequencies such as a VC (Variable Capacitor) seen below.

    So--I just said some words that you might not yet be familiar with: Electric Flux and Capacitance.
    Capacitance:  is an expression of the ratio between the amount of current flowing and the rate of voltage change across the plates of a capacitor.

    Electric Flux: an electric field that exist in the space between the plates of the capacitor.

    In a capacitor, the electric flux concentration is multiplied when a dielectric of a certain type is placed between the plates. Plastics work very well for this purpose. This increases the effective surface area of the plates, so that a physically small component can be made to have a large capacitance. The voltage that a capacitor can handle depends on the thickness of the metal sheets or strips, on the spacing between them, and on the type of dielectric used. Capacitance is directly proportional to the surface area of the conducting plates or sheets. Capacitance is inversely proportional to the separation between conducting sheets; in other words, the closer the sheets are to each other, the greater the capacitance. The capacitance also depends on the dielectric constant of the material between the plates. A vacuum has a dielectric constant of 1; some substances have dielectric constants that multiply the effective capacitance many times.

    Let’s build a capacitor from scratch and see how and if it will work with a project that we'll do.


    In the next chapter, I'll start out with building a cap from scratch and adding it to a circuit if we can. This will be fun to do, and you'll learn quite a bit about how the Capacitor works.

    Until I rebuild and replenish my electronics shop, which recently suffered from a fire, this will have to wait--but I'm very excited about continuing the series.

    Hope you enjoyed this chapter--and as always, if you have any questions, please feel free to ask away.



    Maxhirez's picture

    Geez, Jax-way to give away what they charge thousands of dollars for at engineering school!  If I'd have had you to explain this to me when I was having my first fling with electronics I might be a rich man now.  Anyway, well done and thank you!

    BTW, here's a cheat page for resistor decoding.  I know it's easy to memorize after a while but at 11:00 at night when your eyesight and patience are failing, just picking the colors with your mouse is a lot less troublesome.

    Graphical Resistance Calculator

    GWJax's picture

    Thanks Max for you great comment.. And thanks for sharing the calculator for everyone to use. Your right this is an easier way to find the values when your eyes are crossed from building electronic circuit boards all night, like I would know how that is.. hehe


    BTW as you can see I'm now online with a new laptop but I'm still very long away with getting my supplies back up. My home is being rebuilt and will take up to 7 months to complete so I'm living in an apartment right now and trying to keep things light until I move back into the home.. Cant wait for that...