# Labs from Chicago, Winter 1994 : Ohm's Law.

Dr. Rich Kron, Dr. Heidi Newberg, and Luisa Rebull
Labs written for the CARA Space Explorers, Winter 1994

This is meant to be handed out to the students.

## I. Introduction

In this lab we will quantify certain aspects of electrical circuits by using a multimeter to measure the actual values of voltage V, current I, and resistance R.

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

## II. Resistor Color Codes

We will be using resistors a lot in building our circuits, and it is worthwhile to learn a shorthand system for identifying the value of the resistance, in ohms, for any resistor that you encounter.

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 	9
```
Starting 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.

## III. Using the Multimeter

In the previous part, we wrote down the manufacturer's claim for the resistances of a bunch of resistors. In this part, we will make direct measurements with a gadget called a multimeter. Check that the meter is OFF, that the black probe is plugged into the hole marked "COM," and that the red probe is plugged into the hole marked VW . Now rotate the dial to the W symbol and hold the ends of the probes in your fingers; the meter should read a few MW - this is your resistance to electrical current. Now, touch one probe to the metal wire on one side of a resistor, and the other probe to the other metal wire (the wires attached to electrical components are often called "leads"). The meter will read the resistance in ohms. Write this measured value in the table on the previous page. Check the values you obtained in the previous section from the color bands. Are there any cases where your measured value is more than 10% different from the manufacturer's claimed resistance?

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.

## IV. Ohm's Law

It is important that the values for voltage, current, and resistance in a circuit depend on each other - if you know any 2 of these 3 quantities, you can calculate the third; it can't be an arbitrary value.

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!

## V. Series Circuits

Now let's make a circuit that combines two batteries and two resistors, as shown in Figure 2. Note that you connect the negative terminal of one battery to the positive terminal of the other, but it does not matter which battery goes where. The points marked A, B, C, and D are any convenient places to measure with the multimeter - they don't mark new circuit components. R1 and R2 indicate two resistors; they should be different from one another, but not by a large factor - it is OK to mix a 1 kW resistor with a 10 kW resistor, but not with a 1 MW resistor.

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

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?