Electricity

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Four quantities describe most everyday electrics. Voltage is the push that drives a current, measured in volts: a phone charger gives 5 V, a car battery 12 V, a UK socket 230 V. Current is how much electricity flows, measured in amperes (amps). Resistance is how hard a part makes it for current to flow, measured in ohms. And charge is an amount of electricity, a current kept up for a time, which is what a battery holds and is rated in amp-hours.

Volts and amps

A voltage is written V, volt or volts, and a current A, amp, amps, ampere or amperes. The prefixes a meter shows are there too: mV and kV for thousandths and thousands of a volt, mA and kA for the amp.

12 V // 12.00 V
12 volts // 12.00 volts
230 V in kV // 0.23 kV
500 mA in A // 0.50 A
5 amps in mA // 5,000.00 mA

Ohms

A resistance is written ohm or ohms, or with its symbol Ω, and a resistor’s label usually carries a prefix: kΩ for thousands of ohms and MΩ for millions. The symbol reaches a line as one of two characters that look the same, the Greek capital omega (U+03A9, what a keyboard or a character picker gives) and the ohm sign (U+2126, which a datasheet pasted from a PDF can carry). Both are read as the ohm, and the lower-case omega ω is not.

10 ohm // 10.00 ohm
10 Ω // 10.00 Ω
4.7 kΩ in ohm // 4,700.00 ohm
1 MΩ in kΩ // 1,000.00 kΩ

Ohm’s law

Voltage, current and resistance are tied together: the voltage across a part is its current times its resistance. That is Ohm’s law, and it works in every direction, so dividing a voltage by a current gives the resistance, and dividing a voltage by a resistance gives the current. The engine names each answer, and a voltage times a current is the power in watts.

12 V / 2 A // 6.00 Ω
2 A * 6 Ω // 12.00 V
12 V / 6 Ω // 2.00 A
2 mA * 4.7 kΩ // 9.40 V
230 V * 13 A // 2,990.00 W
2990 W / 230 V // 13.00 A

A quantity named this way is an ordinary one, so in converts it to another unit of the same kind: 12 V / 2 A in kΩ is 0.006 kilohms.

Amp-hours and batteries

A charge is a current for a time. One amp for one hour is an amp-hour (Ah), and a phone battery is rated in thousandths of one, milliamp-hours (mAh). A current multiplied by a time is named in amp-hours, and a charge over a time gives the current back.

3000 mAh in Ah // 3.00 Ah
2 A * 3 h // 6.00 Ah
3 Ah / 6 h // 0.50 A

A battery’s energy is its charge times its voltage, and that is the figure a battery is compared on, in watt-hours (Wh). A charge written in amp-hours at a voltage is named in watt-hours whatever its prefix, so a 3,000 mAh phone battery at 3.7 V holds 11.1 Wh. Dividing a watt-hour energy by a voltage gives the charge back in amp-hours.

3000 mAh * 3.7 V // 11.10 Wh
100 Ah * 12 V // 1,200.00 Wh
100 Ah * 12 V in kWh // 1.20 kWh
11.1 Wh / 3.7 V // 3.00 Ah

The SI unit of charge is the coulomb, one amp for one second, so an amp-hour is 3,600 coulombs. It is written as a word, coulomb or coulombs, because C is Celsius. A charge worked out by arithmetic is always named in amp-hours, even over seconds, so ask for coulombs when that is the unit you want. A charge written in coulombs at a voltage stays in joules, the energy’s own unit.

1 Ah in coulombs // 3,600.00 coulombs
2 A * 30 s // 0.02 Ah
2 A * 30 s in coulombs // 60.00 coulombs
60 coulombs * 12 V // 720.00 J

The boundary

A charge over a current is a time (how long a battery lasts at a steady draw), but it is not named as one, in the same way that an energy over a power is not: both stay as the quotient of the units written. Naming a time from other quantities is a separate piece of work on multiplying and dividing units.

3000 mAh / 500 mA // 6.00 mAh/mA

C stays Celsius, so the coulomb has no symbol. The as readouts of named derived units (as W, as kWh) gain no new names for the ohm, the amp or the amp-hour, because they are matched without regard to case and mΩ and MΩ would be one name; in converts any of them. Capacitance (farads) and inductance (henries) are not units here.