Ohm's Law

We've previously introduced the ideas of current and potential. To review:

• Current is the rate of flow of charge, measured in Amps (coulombs per second).We are going to use the letter I to represent current.
• Voltage is the amount of energy carried by each coulomb of charge in the circuit. It is measured in volts, which is shorthand for joules per coulomb. You can think of voltage as a kind of pressure, pushing charge through a circuit. We are going to use the letter V to stand for voltage.

As the electrons move through the wires of the circuit, they constantly run into the stationary atoms of the wire itself. Those darn atoms are getting in the way, and they hinder, or resist, the flow of the current. How hard they resist the flow is called resistance, and we're going to use R as the variable representing resistance.

The greater the voltage pushing current through a circuit, the more current will flow. They are directly proportional to each other. Conversely, the greater the resistance, the less current flows: they are inversely proportional. Writing this in equation form gives us Ohm's Law:

which can also be written as

Resistance  What are the units used to measure resistance? We can figure this out by solving Ohm's Law for R. That gives us

so the units of resistance would be the unit of voltage (the volt) divided by the unit of current (the amp). This unit gets used so often, though, that it is convenient to have a special, one-word name for it: it's called the ohm, and the symbol for it is the Greek upper-case omega, Ω .

Larger units of resistance are the kilohm (kΩ, equal to 1000 ohms) and the megohm (MΩ, equal to 1,000,000 ohms).

Mnemonic Device  As an aid to your memory, and to save some time doing algebra, remember this circle:

If you need to calculate V, cover the V with your thumb, and you'll see IR. If you need to calculate I, cover it and what's left is V/R. And if you need to calculate R, cover it to reveal V/I.

Example  What is the resistance of a lightbulb which, when connected to a 6-volt battery, has a current of 0.3 amps flowing through it?

Example  How much current will flow through a device with a resistance of 2.2 kΩ when connected to a 12-volt battery?

You can also write this as 5.5 mA (milliamps). Notice that we had to put the resistance value into the equation in ohms, not kilohms.

Conductors & Insulators  All electronic devices, even including plain wire, resist the flow of current to some extent. Materials with a very low resistance are called conductors. Examples include copper, silver, gold, aluminum, and other metals. Materials that have very high resistance, such as rubber, paper, wood and air, are called insulators. Materials that are somewhere in between, such as specially-prepared types of silicon and germanium, are called semiconductors. Semiconductors are the basis for diodes, transistors, and "chips" --- but that is a big topic we'll get to another time.

Resistors  There are many situations in the design of electronic circuits, where it is necessary to limit the amount of current flowing through a wire. A resistor is an electronic component that is designed to have a specific, calibrated resistance value, that allow a designer to tailor the current flowing through a circuit. Most resistors look similar to the photo below, having three or four colored stripes. The stripes are a code that tells what its resistance is. To understand the code, first memorize these correspondences between colors and digits.

0 = BLACK
1 = BROWN
2 = RED
3 = ORANGE
4 = YELLOW
5 = GREEN
6 = BLUE
7 = VIOLET
8 = GRAY
9 = WHITE

Notice that 2 through 7 are the colors of the visible spectrum i.e., the rainbow, ROYGBV (with no "indigo").

Here's how the code works:

• The first two stripes tell you the first two digits of the resistance.
• The third stripe tells you a power of ten to multiply by, or equivalently, how many zeros to tack on.
• The background color of the resistor has no significance, and is not part of the code.

Here's an example: The first three stripes of the resistor pictured below has are GREEN-BLUE-BROWN. The first two stripes give us the digits 5 and 6, and the BROWN third strip says to multiply by 10¹, which is just 10. So this resistor's value is 560 ohms.

The fourth stripe tells you the "tolerance" of the resistor. A GOLD fourth stripe (like the resistor above has) means the manufacturer guarantees the actual resistance is within 5% of the color code value. Continuing the example above, 5% of 560 ohms is 28 ohms. So the manufacturer is guananteeing that the actual resistance is somewhere between 532 ohms (= 560-28) and 588 ohms (=560+28).

If the fourth stripe is SILVER, the tolerance is 10%, and if there's no fourth stripe, the tolerance is 20%.

Here's an applet that you can use to practice decoding resistor values.

3. What are the color stripes for resistors with the following values, all with a tolerance (accuracy) of 5%?

(a) 220 Ω
(b) 1.5 kΩ
(c) 4.7 MΩ

4. What is the resistance, and accuracy, of a resistor with the following stripes?

(a) brown-black-yellow-silver
(b) green-blue-blue-gold
(c) orange-orange-orange

Additional Activities & Practice

5. What are the color stripes for resistors with the following values?

(a) 470 Ω ± 5%
(b) 2.0 MΩ± 20%
(c) 1.5 MΩ± 10%

6. What is the resistance, and tolerance, of a resistor with the following stripes?

(a) brown-red-yellow-gold
(b) blue-grey-yellow
(c) brown-black-brown-silver

7. If you have a 5-volt power supply, and you want to limit the current to 15 mA (0.015 A), what value resistor should you use?

8. If you have a 1.2 kΩ resistor with 150mA of current running through it, what voltage must be driving the current through it?

Check your ANSWERS after you've done all the problems.