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Electrical Units

Current, voltage, and resistance - the quantities, their units, and the two equations that connect them.

  1. Current, Voltage, and Resistance
Engineering Fundamentals/Electrical Quantities

Current, Voltage, and Resistance

The three quantities every schematic and nameplate uses, the units they are measured in, and the two equations that connect them.

Three quantities, three units

Three quantities, three units

Almost every electrical number you will read off a nameplate, a meter, or a schematic is one of three quantities. Each has a name, a quantity symbol used in formulas, and a unit symbol written after a value.

Current, I
The rate at which electric charge flows past a point. Its unit is the ampere, symbol A — one of the seven SI base units. One ampere is one coulomb of charge per second.
Voltage, V
Also called electric potential difference: the difference in electric potential between two points. Its unit is the volt, symbol V, defined as power per unit of current.
Resistance, R
How strongly something opposes the flow of current. Its unit is the ohm, symbol Ω, defined as voltage per unit of current.
How each unit is built out of the others.
QuantityUnitSymbolIn other units
Electric currentampereASI base unit; 1 A = 1 C/s
Electric chargecoulombCs·A
Potential differencevoltVW/A, and so (N·m)/(A·s)
ResistanceohmΩV/A, and so W/A2

Say “amp” if you like; write A. The unit name is the ampere, and the symbol is a capital A because the unit is named after a person. So is the volt (V) and the watt (W). Lower case changes the meaning of a prefix, not just the look of it: mA is a milliampere and MA is a megaampere, a billion times larger. See Measurement Language.

Supporting detail: Addendum 1 — Why voltage and resistance are called derived units.

Two equations, and everything else follows

Two equations, and everything else follows

For an ohmic resistor (constant resistance under the stated conditions), the set is generated by Ohm’s law and the power relationship:

V = IR  —  P = VI

Rearranging and substituting gives three expressions for each of the four quantities. There is nothing to memorise beyond the two above; the table is a lookup, not a list of new facts.

Resistive-load magnitudes: steady DC, or RMS voltage and current for AC.
To findFrom V and I or RUsing powerUsing power
Voltage, VV = IRV = P/IV = √(PR)
Current, II = V/RI = P/VI = √(P/R)
Resistance, RR = V/IR = V2/PR = P/I2
Power, PP = VIP = I2RP = V2/R

P = VI gives real power in watts on direct current or a purely resistive load. For single-phase AC, RMS volts times RMS amps is apparent power in volt-amperes, and the real power is that multiplied by the power factor — see Power and Efficiency.

Worked example: what a lamp draws

Worked example: what a lamp draws

How much current does a 100 W resistive lamp draw on a 120 V supply (RMS for AC)?

  1. Pick the form with the two quantities you have: I = P/V.
  2. I = 100 W ÷ 120 V = 0.833 A.

Check the units rather than trusting the arithmetic. A volt is a watt per ampere, so watts divided by volts leaves amperes — which is what was asked for.

Worked example: voltage drop along a cord

Worked example: voltage drop along a cord

A 100 ft extension cord has a total out-and-back conductor resistance of 0.1588 Ω. What is the resistive voltage drop across that path when 10 A flows through it?

  1. V = IR = 10 A × 0.1588 Ω = 1.588 V.

About 1.6 V. That is 1.6 V that never reaches the tool: for DC or an AC resistive load, the supply voltage equals the cord drop plus the load voltage.

Supporting detail: Addendum 2 — The dropped voltage does not disappear.

The same method keeps working

The same method keeps working

These are not the last units you will meet. Each new quantity arrives the same way: it is defined as a combination of quantities you already have, and its unit is that same combination.

A few more, and where each one comes from.
QuantityDefined asSI unit
Pressure or stressForce per unit areapascal, Pa = N/m2
Volumetric flow rateVolume per unit timem3/s
Specific weightWeight per unit volumeN/m3
CapacitanceCharge per unit voltagefarad, F = C/V

Read the middle column and the right-hand column together and the pattern is the whole point: the unit is the definition, written in symbols. Once that clicks, a unit you have never seen tells you what the quantity is.

Sources

Sources

Supporting detail: Addendum 3 — Where these values were checked.

Supporting detail

Addendum

Additional evidence, standards context, and background referenced from the main text.

  1. Engineering Fundamentals/Electrical Quantities/Current, Voltage, and Resistance

    Addendum 1. Why voltage and resistance are called derived units

    Of the four units above, only the ampere is a base unit — one of the seven that the rest of SI is built from. The others are derived: their definitions are ratios of units already defined. NIST expresses the volt as W/A and the ohm as V/A, and traces both back to base units as m2·kg·s−3·A−1 and m2·kg·s−3·A−2.

    That is why unit cancellation works on electrical problems exactly as it does on mechanical ones — the electrical units are made of metres, kilograms, seconds, and amperes underneath. The technique on Dimensional Analysis does not need a separate electrical version.

    Back to reference 1

  2. Engineering Fundamentals/Electrical Quantities/Current, Voltage, and Resistance

    Addendum 2. The dropped voltage does not disappear

    The power lost in the cord is P = I2R = (10 A)2 × 0.1588 Ω = 15.9 W. That power becomes heat in the conductor, spread along its whole length.

    Notice the squared current. Doubling the load to 20 A does not double the loss, it quadruples it, to about 64 W. This is why the drop that is harmless on a light load becomes a real problem on a heavy one, and why the length and gauge of a cord matter more the more current the tool draws. The condition and routing of the cord itself are covered on Electrical Safety.

    Back to reference 2

  3. Engineering Fundamentals/Electrical Quantities/Current, Voltage, and Resistance

    Addendum 3. Where these values were checked

    NIST SP 811, Chapter 4, Table 3, gives: volt V, expressed as W/A, base units m2·kg·s−3·A−1; ohm Ω, expressed as V/A, base units m2·kg·s−3·A−2; coulomb C, base units s·A; watt W, expressed as J/s; pascal Pa, expressed as N/m2; and farad F, expressed as C/V.

    The ampere is listed as one of the seven SI base units, with symbol A, by both BIPM and NIST. The rule that a unit symbol takes a capital first letter when the unit is named after a person is NIST SP 811, Chapter 6.

    Back to reference 3