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T5B

ELECTRICAL PRINCIPLES

Math for electronics: conversion of electrical units, decibels

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T5B011 of 13

How many milliamperes is 1.5 amperes?

Why The prefix milli- means one thousandth, so 1 milliampere is 0.001 ampere and 1 ampere is 1000 milliamperes. Converting from the larger unit to the smaller one means multiplying, so 1.5 x 1000 = 1500 milliamperes.
Watch out The tiny values like 0.0015 come from dividing by 1000 instead of multiplying, which is the conversion you would use going from milliamperes to amperes. The 1,500,000 figure would be microamperes, since micro- is one millionth.
Going to a smaller unit, the number gets bigger: amps to milliamps, multiply by 1000.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
T5B022 of 13

Which is equal to 1,500,000 hertz?

Why Metric prefixes just move the decimal point: kilo means one thousand, so 1 kHz = 1,000 Hz. Dividing 1,500,000 Hz by 1,000 gives 1500 kHz, which is the same as 1.5 MHz since mega means one million.
Watch out 1500 MHz sounds similar but means 1,500,000,000 Hz, a thousand times too big; 150 kHz is only 150,000 Hz, ten times too small.
Hz to kHz, drop 3 zeros; kHz to MHz, drop 3 more. 1,500,000 Hz = 1500 kHz = 1.5 MHz.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
T5B033 of 13

Which is equal to one kilovolt?

Why The prefix kilo- always means one thousand, so a kilovolt is 1000 volts, just as a kilometer is 1000 meters and a kilohertz is 1000 hertz. To convert kilovolts to volts you multiply by 1000; to go the other way, divide by 1000.
Watch out One one-thousandth of a volt is a millivolt (milli-), and one million volts would be a megavolt (mega-). Watch for the letter case too: lowercase k is kilo, uppercase M is mega.
k = 1000 (kilometer = 1000 m). Small prefixes are milli/micro; big ones are kilo/mega/giga.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
T5B044 of 13

Which is equal to one microvolt?

Why The prefix micro always means one millionth, or 10^-6. So one microvolt is 0.000001 volt, and conversely 1 volt equals 1,000,000 microvolts. Microvolts show up when describing very weak receiver input signals.
Watch out One one-thousandth of a volt is a millivolt (milli = 10^-3); the choices with millions of volts confuse the prefix with mega, which multiplies instead of divides.
Micro shrinks by a million, milli by a thousand, mega grows by a million.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
T5B055 of 13

Which is equal to 500 milliwatts?

Why The prefix milli means one thousandth, so to convert milliwatts to watts you divide by 1000. 500 / 1000 = 0.5 watt. Going the other way, multiply watts by 1000 to get milliwatts.
Watch out The choices in the hundreds of thousands or millions come from multiplying by 1000 instead of dividing; that would be the conversion for kilowatts or megawatts, which are larger units, not smaller ones.
Milli = thousandth. Small prefix means a smaller number of watts, so divide by 1000 and the decimal moves left.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
T5B066 of 13

Which is equal to 3000 milliamperes?

Why The prefix milli means one thousandth, so 1000 milliamperes make 1 ampere. Dividing 3000 mA by 1000 gives 3 A. Going from a smaller unit (mA) to a larger unit (A), the number always gets smaller.
Watch out The choice showing 0.003 amperes comes from multiplying by 1/1000 twice, or from confusing 3000 mA with 3 mA; 0.003 A is only 3 milliamperes.
Milli means move the decimal 3 places: mA to A, divide by 1000. 3000 mA = 3 A.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
T5B077 of 13

Which is equal to 3.525 MHz?

Why Kilo means thousand and mega means million, so 1 MHz equals 1,000 kHz. Multiplying 3.525 by 1,000 shifts the decimal point three places right, giving 3525 kHz (which is also 3,525,000 Hz). This is a common ham frequency in the 80 meter band.
Watch out The choice of 3,525,000 is the value in hertz, not kilohertz; that would only be right if the unit were Hz. Dividing instead of multiplying gives the tiny 0.003525 figure.
MHz to kHz: move the decimal three places RIGHT (x1000). Going to a smaller unit always makes the number bigger.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
T5B088 of 13

Which is equal to 1,000,000 picofarads?

Why Pico means 10^-12 and micro means 10^-6, so there are 1,000,000 picofarads in one microfarad. Dividing 1,000,000 pF by 1,000,000 gives 1 microfarad (which is also 10^-6 farad). Converting from a smaller prefix to a larger one always makes the number smaller.
Watch out The choice saying 1000 microfarads comes from moving the decimal only three places, as if pico and micro were one step apart; they are two steps (pico, nano, micro), a factor of a million.
pico to micro = move 6 places: 1,000,000 pF = 1000 nF = 1 uF.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
T5B099 of 13

Which decibel value most closely represents a power increase from 5 watts to 10 watts?

Why Decibels compare powers on a logarithmic scale: dB = 10 x log(P2/P1). Going from 5 W to 10 W is a ratio of 2, and 10 x log(2) = 3.01, so about 3 dB. Doubling power is always close to 3 dB no matter what the starting wattage is.
Watch out The choice of 2 dB comes from mistaking the power ratio of 2 for the decibel number, and 5 dB looks like the 10 minus 5 difference in watts, but decibels come from the ratio put through a logarithm, not from subtraction.
Double the power = +3 dB, half the power = -3 dB. Ten times = 10 dB.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
T5B1010 of 13

Which decibel value most closely represents a power decrease from 12 watts to 3 watts?

Why Decibels compare powers as a ratio, not a difference. Going from 12 W to 3 W is a ratio of 1/4, and each halving of power is -3 dB, so two halvings give -3 dB + -3 dB = -6 dB. Formally, 10 log(3/12) = 10 log(0.25) = -6 dB.
Watch out The choice of -3 dB would be right only if the power dropped by half, to 6 watts; subtracting 12 - 3 = 9 and reading it as -9 dB confuses a difference with a ratio.
Half = 3 dB, quarter = 6 dB, tenth = 10 dB. Count doublings or halvings, not watts subtracted.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
T5B1111 of 13

Which decibel value represents a power increase from 20 watts to 200 watts?

Why Decibels compare two power levels using dB = 10 log10(P2/P1). Going from 20 W to 200 W is a ratio of 10, and log10(10) = 1, so the result is 10 dB. A factor of 10 in power is always 10 dB, no matter what the starting wattage is.
Watch out The larger values like 18 dB or 28 dB would mean much bigger ratios (about 63 times and 630 times the power); people sometimes pick them by wrongly subtracting or adding the watt numbers instead of taking the ratio.
Power times 10 = +10 dB, times 2 = +3 dB, half = -3 dB, tenth = -10 dB.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
T5B1212 of 13

Which is equal to 28400 kHz?

Why Kilo means thousand and mega means million, so 1 MHz = 1000 kHz. To convert kilohertz to megahertz you divide by 1000, which moves the decimal point three places left: 28400 / 1000 = 28.400 MHz. That lands in the 10 meter band, a familiar HF frequency.
Watch out The choice reading 2.800 MHz shifts the decimal four places instead of three, and 284.00 MHz multiplies instead of divides; kHz to MHz always makes the number smaller.
kHz to MHz: slide the decimal 3 places LEFT. 28400 kHz becomes 28.400 MHz.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
T5B1313 of 13

Which is equal to 2425 MHz?

Why Metric prefixes step by factors of 1000: 1 GHz = 1,000 MHz. So to convert megahertz to gigahertz you divide by 1000, moving the decimal point three places left, and 2425 MHz becomes 2.425 GHz. This is the popular 2.4 GHz band used for Wi-Fi and amateur microwave work.
Watch out The choice showing 0.002425 GHz comes from dividing by a million instead of a thousand, which would be the kHz to GHz jump; 24.25 and 242.5 GHz move the decimal the wrong direction.
Going up a prefix (M to G), divide by 1000: the number gets smaller. 2425 MHz is the familiar 2.4 GHz band.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
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