Current, Voltage, and Resistance

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.

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.

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.

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.

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

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

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.

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.

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.

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.