Thursday, July 16, 2009

Amateur Radio license exam prep - The Arithmetic

The amateur radio technician exam is mostly about memorizing rules and facts. As such, the best advice I can give is to go visit the AA9PW practice exam generator page and take the test repeatedly until you stop regularly failing it. It's actually not that hard to guess most of the answers. The ones you can't guess, you can just learn by repetition as you keep taking the practice tests.

There is, however, some math you should learn how to do rather than memorize, as it is easier. The laws of physics that embody the math you need to learn are embodied by 3 basic formulae. They are, E=IR, P=IE, and C=λω

Now, I can see some of your eyes have just glazed over. But bear with me. It's not that hard. Honest.

The first formula is E=IR, which is known as Ohm's Law. It's the relationship between the voltage drop across a load of a given resistance with a given amount of current flowing through it.

E, perversely enough, is the mathematical symbol for voltage. No, it's not V, 'cause that one was taken (Volume). It's E. You'll just have to remember that one. Voltage is electrical potential, more or less. People often compare voltage and current to water running through hoses. Voltage is analogous to the water pressure.

I, again, perversely enough, is the mathematical symbol for current. Electrical current is measured in Amperes, or Amps for short. Current, using the same water analogy, is how much water moves through the hose in a given time.

R is electrical resistance. Resistance is measured in units called Ohms, denoted by the greek letter Ω.

The basic formula is listed as E=I×R, but if you divide both sides of the equation by R, you get I=E÷R. Divide both sides by I and you get R=E÷I. If you think of those divisions as fractions, then you wind up with this little graphic symbol you can use to remember the relationship:

So that circle represents the relationship. If you remove from the circle the unknown you want to solve for, what's left tells you what the rest of the equation will look like. For example, if you remove the I, you're left with E over R, or E÷R. If you remove the E, you're left with I next to R, or I×R.

So, take question T4D04, for example:

What is the resistance of a circuit when a current of 3 amperes flows through a resistor connected to 90 volts?

A. 3 ohms
B. 30 ohms
C. 93 ohms
D. 270 ohms

They want to know R, and they've supplied you with I and E. R=E÷I. In this case, R=90÷3, or 30. The answer is B.

The next formula relates voltage and current to power. Power is P, and is measured in Watts. I and E are current and Voltage, just like before. P=IE. And like before, the circle chart can be used to figure out all of the relationships:

Let's use question T4E06 as an example:

How many amperes are flowing in a circuit when the applied voltage is 120 volts DC and the load is 1200 watts?

A. 20 amperes
B. 10 amperes
C. 120 amperes
D. 5 amperes

They want to know the current (Amperes), and they've given you the power and voltage. I=P÷E. Or, in this case, I=1200÷120: 10. The correct answer is B.

The last one looks a little funnier, but in truth it's actually easier. The formula is C=λω - the speed of light is equal to the frequency of a wave times its wavelength. Well, the speed of light is 300,000,000 meters per second, or 300 million meters per second. Wavelengths are in meters, at least for the purpose of this exam, and frequency is measured in Hertz (abbreviated as Hz). One Hz is one cycle per second. If we divide both sides of the equation by a million, you wind up with the formula 300 = frequency in Mhz × wavelength in meters. We can make a circle chart up for that one too:

In this case, we will never have the 'top' of the chart be an unknown, so we wind up with only two formulas, both of which look the same: You divide 300 by either the frequency in MHz or the wavelength in meters, and you get the other value.

Take question T1C05:

Which amateur band are you using when transmitting on 146.52 MHz?

A. 2 meter band
B. 20 meter band
C. 14 meter band
D. 6 meter band

300÷146.52 is approximately 2. The correct answer is A.

This formula can also be used to figure out antenna lengths. Take question T9A11:

What is the approximate length, in inches, of a quarter-wavelength vertical antenna for 146 MHz?

A. 112 inches
B. 50 inches
C. 19 inches
D. 12 inches

146 MHz is 2 meters. A quarter wavelength is half a meter. Half a meter is about half a yard, or a foot and a half or about 18 inches. The correct answer is C.

And that's it. So far as I know, that's all the math you need to know and understand to pass the technician exam. All the rest of it is just rote memorization of facts and rules.

Good luck!

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