Lesson 5 Ohm's Law Exercises
Let's do some lab problems with resistors.
Before we do some problems, lets learn how to read resistor color codes.
Most of the time you will probably use resistors with 4 bands in their color code. Here is a typical resistor:
This happens to be a 1000 ohm resistor, or commonly referred to as a "1K"
The brown band stands for 1, the black band stands for 0, and the red band means you put 2 zeros after the first two digits: 1-0-00 or 1,000 ohms.
Resistors are usually never the exact value as the color code indicates so the manufacture uses the fourth band to indicate the tolerance of the resistor. In theis case, the silver band corresponds to a 10 percent tolerance. It is pretty rare to find a 10 percent tolerance on a resistor nowdays. Most resistors nowdays carry a 5 percent tolerance which corresponds to a gold band.
Precision resistors are sometimes used in critical locations. They use a 5 band color coding system, but we won't worry about those right now.
To calculate the value of a resistor using the color coded stripes on the resistor, use the following procedure.
"Step One: Turn the resistor so that the gold or silver stripe is at the right end of the resistor.
Step Two: Look at the color of the first two stripes on the left end. These correspond to the first two digits of the resistor value. Use the table given below to determine the first two digits.
Step Three: Look at the third stripe from the left. This corresponds to a multiplication value. Find the value using the table below.
Step Four: Multiply the two digit number from step two by the number from step three. This is the value of the resistor in ohms. The fourth stripe indicates the accuracy of the resistor. A gold stripe means the value of the resistor may vary by 5% from the value given by the stripes."
Here is a color code chart. It's funny, but just about every tutorial I have seen fails to mention one very important memorization fact: The color code is arranged like the colors of the rainbow! The last two bands, gold and silver, do not apply to this. I usally forget the order of the green and blue color bands all the time, so I have to revert back to the rainbow. Green comes before blue:
Resistors do not come in an ifinite number of values, so eventually, you will be able to recognize their value at fisrt sight, without having to do the math in your head. This is especially true with common values like 100 ohms, 1 K, 10 K, 100 K, 1 Meg (Meg=million ohms), 47 K, etc.
Grab about ten different resistors and practice the color code. Verify your guesses with an ohm meter. You will get it down pretty quickly. And remember the rainbow trick!
An easier way to use the third band which is the multiplier, is to just add the number of zeros that the band corresponds to after you figure out the first two digits. Example: Brown-Black-Orange corresponds to a 10 with an "orange" amout of zeros after it. Orange corresponds to 3 on the color code chart, so you have a 10 with 3 zeros after it, which is, of course, 10,000, or a 10 K resistor.. Thie eliminates they typical multiplication method, which is a pain in my opinion.
Here is a resistance calculator. You can play around with it to get familiar with color codes. You can pull down different colors from the menus at the top:
OK, lets solve a series circuit problem.
Some properties of
Series Circuits:
1. Current only has one path.
2. Current is the same everywhere.
3. Voltage drop across each resistor in a series circuit depends on the value of the resistor. The higher the value, the higher the voltage drop.
4. The sum of all the voltage drops across the resistors in a series circuit is equal to the applied voltage from the power supply or battery.
Connecting resistors in a string one pigtail to another is called connecting them in series. When connected this way the resistance of one resistor adds to the next in line. For example a 100 ohm resistor in series with a 500 ohm resistor is the same as having a 600 ohm resistor.
OK, lets do a series circuit problem. Here is the circuit. Just a battery and two light bulbs in series:
Light bulbs are nothing more than resistors that put out light. So we can re-draw the circuit and just denote the light bulbs as resistors. We will also use the symbol for a battery. By the way, the larger bar of a battery symbol always denotes the positive terminal:
OK, so lets do a little math using Ohm's law and the properties of a series circuit to analyze this thing.
Ohm's Law: E=IR. where E equals voltage. I is current, and R is resistance.
Lets find the current flowing thru this circuit. Remember that the current flowing thru a series circuit is always the same. So if we find the total current, we will have the current flowing thru both of the resistors. To find the current, we need to know the voltage applied to the circuit, and the total resistance of the circuit. In a series circuit, we simply add up the resistances. In this case, the total resistance is 9 ohms plus 6 ohms equals 15 ohms total. Now we have enough variables to compute the current, as the battery voltage has been given as 30 volts.
Ohm's Law: E=IR We want to find the current in this circuit, so let's put the current variable on one side of the equation:
I=E/R, punching in our numbers we have I = 30/15 = 2 Amps.
Here is the equivalent of our lightbulb circuit:
Let's figure out a few more things about this circuit. That 30 volts from the battery has to be chewed up by the two resistors. But which resistor do you think chews up the most voltage? We can find out by using the fact that current is always the same in a series circuit, and with ohm's law.
The voltage across the resistors is going to be E=I x R, so lets punch in the values to get some answers: For the 9 ohm resistor, the voltage across it will be the current thru it times it's resistance, so E = 2 amps x 9 ohms, which is 18 volts.
The voltage across the 6 ohm resistor will be caculated the same way, so E = I x R, so E = 2 amps x 6 ohms, which is 12 volts.
Now since the two resistors have to chew up the 30 volts from the battery, adding up the two different voltage drops across them should give us the battery voltge: 18 + 12 is indeed, 30 volts! So we know we have done our math right.
Notice that the 9 ohm resistor chews up more voltage than the 6 ohm resistor, as it offers more opposition to the 30 volt battery.
By the way, which resistor do you think is going to get hotter? We have not studied the power formula, but we should still be able to make a guess; Well, both resistors have the same amount of current flowing thru them because they are in series. But one is only holding back 12 volts, and the other has to hold back 18 volts. Which one do you think has to work the hardest?
You can practice your Ohm's Law by changing the values of the above circuit and re-computing. Then, add more resistors and do some more problem solving.
Let's do a
Parallel Circuits problem.
Properties of Parallel Circuits:
1. Voltages is the same.
2. Current varies.
3. Total resistance decreases with more resistance.
A parallel circuit is a current divider.
In this illustration you can see that the sum of the individual currents, Ib, Ic and Id, will add up to the total current, Ia:
Here is a parallel circuit.
In this case, the two resistors have the same value, 10 ohms each. We would expect the current flowing in the circuit to be divided equally among the two resistors, no? We can also speculate that the power disapated by each resistor would also be equal. We can use Ohm's Law to calculate the total current flowing in this circuit, just like we did in the series circuit, but there is a twist. How do we calculate the total resistance?
Well, since the electrons have two paths they can take back to the battery, and each of these paths are ten ohms, the total resistance of this circuit is five ohms. What if we were to add a couple more ten ohm resistors in parallel? Well, the total resistance would be 10 ohms divided by four, which is 2.5 ohms.
In fact, if the resistors in a parallel circuit are all the same value, then you can compute the total resistance by simply taking the value of one of the resistors and dividing it by the number of resistors there are in the circuit.
So if you had ten ea. 100 ohm resistors in parallel, the total resistance would be 100 ohms/10 ea., which is 10 ohms.
If you had 50 ea. 1 ohm resistors in parallel, you would have 1 ohm/50 ea. = 1/50 th of an ohm.
So the formula for like resistors in parallel is:
R-total = any R/no. of R's.
One good thing to remember about parallel resistance problems is that the total resistance is ALWAYS less than the value of the smallest resistor. You can use this fact as a quick reality check when you do a parallel resistance problem.
Computing the total resistance of a parallel circuit with resistors of different values is a bit more tricky than a problem with like value resistors. Here is parallel resistance problem with unlike resistors.
Notice that there is twice as much current flowing thru the resitor with half as much resistance. That makes sense, right? There is half as much resistance, therefore twice as much current. Note from the picture that both resistors have 30 volts across them.
Let's use Ohm's Law to make sure that the values on that drawing are correct. We use the same Ohm's Law formula that we used for series circuits, E=IR.
Since the voltage across resistors in a parallel circuit is the same, we use 30 volts for both calculations:
30V/3 Ohms is 10 amps, and 30V/6 ohms is 5 amps.
So the total current flowing is found by adding up the individual currents in the two branches: 10 plus 5 is 15 amps total.
So what is the total resistance of this circuit? We can use the total current and the total voltage applied:
30V/15 amps is 2 ohms total.
Notice that the total resistance of 2 ohms is less than the smallest resistor in the circuit.
There is a formula for calculating total resistance in a parallel circuit:
Let's use it in a couple of examples.
To find the equivalent resistance (the total resistance offered to the flow of current) we invert the values and add them. Then we invert the result.
For example take 2 ohms and 4 ohms in parallel.
Inverted 1/2 +1/4 = 3/4
Invert this 4/3 = 1.33 ohms
A quick check on your answer is that it should be smaller in value than the value of the smallest resistor.
Let's try it out on one more problem:
3 Ohms and 6 ohms in parallel:
Inverted 1/3 + 1/6 = 1/2.
Invert this 2/1 = 2 Ohms. Hey, that's the answer to the problem we did up above, right? (the one with the blue background)
So we know the formula works.
Remember:
Resistors in parallel are connected across one another.
They all have the same voltage across them.
The good news about parallel resistance problems is that in real life, you will seldom encounter problems with more than two resistors in parallel. So practicing on a problem like this is good exercise, but not really necessary, but just in case, let's just do one last problem to make sure we have this down. Here it is. What is the total resistance from A to B?
Try it yourself before you look at the answer.
1/2 + 1/3 + 1/6 + 1/1 = 2. Invert this 1/2 = 0.5 ohms.
Here is a link to a Parallel Resistance Calculator:
http://www.1728.com/resistrs.htm
One last tip for parallel circuits:
If one resistor is at least ten times the value of the smaller resistor in a parallel circuit, it can sometimes be ignored.
Example: If a 10 ohm resistor is in parallel with a 100 ohm resistor, the total resistance is about 9.1 ohms.