Electrical principles: one family of quantities, one line of arithmetic

This topic asks you to name the quantity or the unit that fits a short description, to restate one value in a different metric prefix, and to push a short line of arithmetic through Ohm's law or the power law. The steps are small ones — a multiplication, a division, sometimes two of them in a row — so the marks go on choosing the right operation and the right direction.

One family of quantities, one line of arithmetic

• The prefix ladder runs micro, milli, the bare unit, kilo, mega, giga, and every neighbouring pair differs by a factor of 1000; pico stands lower still, a factor of 1,000,000 below micro. Count the steps between the prefix you were given and the prefix you are asked for before you touch the digits.
• Each step toward a larger unit divides the number by 1000; each step toward a smaller unit multiplies it by 1000. The quantity itself never changes, only the way it is written.
• Prefix symbols carry meaning in their case: a lowercase k is kilo, a capital M is mega, a lowercase m is milli. A unit named after a person takes a capital first letter and lowercase after it, which is why hertz is written Hz.

Two products cover every calculation in this topic. Ohm's law binds the three circuit quantities as E = I × R, and the DC power law binds the supply to what it delivers as P = I × E. Whichever letter a question asks for, isolate it: the two quantities on the right multiply, and the letter you want is recovered by dividing the product by the quantity you already know. Volts, amperes and ohms are different quantities, so adding or subtracting the two numbers in a prompt is never a legitimate step, and in a division the order settles everything — 24 volts across a 6-ohm resistor gives 24 / 6 = 4 amperes, while dividing the other way round returns a tidy fraction that is simply upside down.

Decibels describe the ratio between two power levels, never the levels themselves. Break the ratio into familiar steps and add them up: each doubling of power is worth 3 dB and each factor of ten is worth 10 dB, so a ratio made of several such steps is the sum of their decibels. When the power falls instead of rising, the count is the same and the sign is negative.

Where the marks are lost

• Answering a rate question with a total. Power is a rate and is measured in watts; the choice that multiplies a unit of power by a period of time names the energy that rate delivers over that period, and the other quantities offered beside it describe opposition or flow rather than speed of use.
• Running a prefix in the reverse direction. Restating a value in a smaller unit must make the number bigger, and restating it in a larger unit must make it smaller; distractors are built from the same digits with the decimal point pushed the wrong way, so settle the direction before you count zeros.
• Assuming every prefix jump is a factor of a thousand. Neighbouring steps are, but the gap between the smallest prefixes is wider than that, and a question can also step two rungs at once. A choice that is a thousand times off the right one is offered often enough to be worth checking for.
• Trusting an abbreviation without reading its case. A capital and a lowercase letter can stand for prefixes a billion apart, and a unit named after a person is not written in capitals throughout; in these questions three of the four choices differ from the correct one in case alone.
• Combining volts, amperes and ohms with the wrong operation or in the wrong order. The sum and the difference of the two numbers in the prompt sit among the choices in almost every calculation question and are never the answer, and an inverted division returns a fraction that looks precise and is upside down.
• Guessing a decibel figure instead of counting the steps. Some choices echo the numbers of watts in the prompt as though they were decibel values, others are merely plausible-looking figures; what you need depends on nothing but how many doublings or tenfold steps separate the two power levels, so count them.

Try it yourself