Ohm's Law.

Labs written for the CARA Space Explorers, Winter 1994

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This is meant to be handed out to the students.*

IT IS IMPORTANT TO READ ALL THE DIRECTIONS IN THIS LAB!

Look at the resistors in your lab setup. Each has 4 bands of color; three of these bands form a group towards one end of the resistor, and the fourth is separate, and is always either silver or gold. If the fourth band is silver, it means that the manufacturer's claimed resistance is within 10% of the actual resistance - it's kind of a quality assignment. If the fourth band is gold, it means that the tolerance is 5%. For the moment, we will concentrate on the other three bands.

The bands are coded by assigning a numerical value to each color. The code is as follows:

black 0 green 5 brown 1 blue 6 red 2 purple 7 orange 3 gray 8 yellow 4 white 9Starting from the band closest to the end of the resistor, we might have a resistor with the color sequence brown - black - red. We de-code this as 10 according to the table, which actually means 10 x 10 That is, the third band gives the power of ten that multiplies the number formed from the first two. In this case, 10 x 10 resistor is therefore 1000 ohms (also called 1 kilo- ohm).

Suppose we have a resistor with a resistance of 5.6 ohms. Since this is less than 10, we have to multiply by a number that is smaller than 1. If there is a gold band in the third position, then you multiply by 0.1. That is, a resistor with the color sequence green - blue - gold would decode to 56 x 0.1 = 5.6 ohms.

It is worthwhile to practice this a few times. From the 6 resistors that you selected, write down their color codes, decode it, and finally give the values of the resistance for each in ohms. To help you with this, a few other examples are given.

color sequence de-coded ohms (W ) predicted measured blue-red-black 62 x 100 62 grn-yel-brn 54 x 10^1 540 prpl-wht-blue 79 x 10^6 79 mega-ohms (MW ) orng-orng-gold 33 x 0.1 3.3 _______________ ________ _____ _____ _______________ ________ _____ _____ _______________ ________ _____ _____ _______________ ________ _____ _____ _______________ ________ _____ _____ _______________ ________ _____ _____The symbol for the unit of ohms is Greek omega, or W. A thousand ohms could be written as kW, and a million ohms could be written as MW. You may notice that some resistors are large and some are small, and that the size does not seem to have much to do with the value of the resistance. It turns out that the size is related to how much power the resistor can safely handle - this is something we will discuss later in this course.

***** From your resistors, select any that have values within the range 12 ohms to 120 ohms and put them aside for use later. If you do not have three such resistors, an instructor will help you find some.

The multimeter can also be used to measure the voltage of a power supply such as a battery. To do this, make sure the probes are plugged in the same way as for measuring resistance (black to the hole marked "COM," red to hole marked VW ). Turn the dial to read "V==". (This is for direct current, or DC. The other symbol, V~, is used for measuring alternating current, or AC.) Now, measure the voltage of your battery by connecting the red or + probe to the red or + terminal of the battery, and the black or - probe to the black or - terminal of the battery.

voltage of battery: _______________ volts.

If you get the red and black probes the wrong way, the multimeter will give a reading with a negative sign.

Finally, the multimeter can also be used to measure the current. The unit of electrical current is the amp. The symbol for the unit is A, while the symbol for the concept for current is I. (This is like the symbol for the concept of velocity being V, but the symbol for certain units of velocity is mph.) To measure the current, first turn the multimeter off and move the red probe to the hole marked 10A. Then, put the multimeter into a circuit of the type shown below:

Figure 1 - How to measure the current in a circuit.

Now, rotate the meter dial to A== and read the value for the current in amps. To get a sensible reading, for a 6-volt power supply your resistor should be less than about 120 ohms.

To protect the multimeter, remember the following precautions:

1) When measuring a resistance, make sure there is no voltage applied to the circuit.

2) When measuring a current, don't forget to move the red probe to the other hole (the one marked 10A). This means that the maximum current allowed is 10 amps. But, how do you know before you have made the measurement of current whether the current will be less than 10 amps? That is the topic of the next section ...

3) When measuring voltage, move the dial to volts before hooking up the probes.

Using either the color band technique or direct measurement, find at least three resistors that have resistances in the range 12 ohms to 120 ohms. Enter their measured resistances in the table below. For each one, construct the circuit that is shown above, measure the current in the circuit, and write that down in your table. Notice that when the resistance is high, the current is low, and vice versa. Finally, calculate the product I x R, where I is your measured value for the current (in amps or A) and R is your measured value for the resistance (in ohms -- W ). Enter this in your table too.

current (A) resistance (W) V = I x R _________ ___________ __________ _________ ___________ __________ _________ ___________ __________The heading to the last column is "Ohm's Law:" it says that the voltage is equal to the current times the resistance in a circuit. Since the power supply has not changed, all of the numbers in the last column should be about the same. Are they? They should equal the voltage of your power supply that you measured earlier. Is this the case?

Ohm's Law, V = I x R, is very important, and you need to memorize it!

Figure 2 - A circuit with two batteries in series and two resistors in series.

Without the two batteries connected, measure the resistance between the following points:

AB: R1 = __________ W

BC: R2 = __________ W

AC: R1 + R2 = __________ W .

Does the resistance of the combination of the two resistors (AC) equal the sum of the two resistors taken one at a time (AB + BC)? To describe the way that the two resistors appear in this circuit, we say that they are in series, meaning that the current first flows into one resistor and then into the other.

Before connecting the batteries to the circuit or to each other, measure their voltages (call one V1 and the other V2) and write these down:

voltage of battery V1: __________ V

voltage of battery V2: __________ V .

Now connect the two batteries (which are also said to be in series) according to Figure 2 and measure the voltages between the following pairs of points:

AB: VAB = ____________ V

BC: VBC = ____________ V

AC: V1 + V2 = ____________ V

AD: ____________ V

DC: ____________ V .

Explain why in this table the voltage from point A to point C is called "V1 + V2". Is the sum of the separate voltages of the two batteries equal to the total effect of having both batteries in series?

Finally, we will calculate the currents in different parts of the circuit. Recall that Ohm's Law says that

V = I x R .

This can be re-arranged to be

I = V / R .

Calculate the following quantities:

IAB = VAB / R1 = ______________ A

IBC = VBC / R2 = ______________ A

IAC = VAC / (R1 + R2) = ______________ A .

The result you get should be that the current is the same at every point in the circuit. What would happen if this were not true?

**Important Disclaimers and
Caveats**

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