Units and Standards

Units and dimensions

A measured quantity is expressed as a numerical value and a unit. A unit conversion changes the numerical value while preserving the physical quantity. Dimensional consistency is necessary for a valid equation, although it does not prove the equation is physically correct. Electrical SI units include ampere (A), volt (V), ohm (Ω), siemens (S), coulomb (C), farad (F), henry (H), watt (W), joule (J), weber (Wb) and tesla (T). Useful relations are C = A·s, V = W/A, Ω = V/A, F = C/V, H = V·s/A, Wb = V·s and T = Wb/m². Power and energy are different: 1 kWh = 3.6 × 10⁶ J.

Prefixes

Common prefixes include mega M = 10⁶, kilo k = 10³, milli m = 10⁻³, micro μ = 10⁻⁶ and nano n = 10⁻⁹. Prefix case matters: mΩ and MΩ differ by a factor of 10⁹. For area conversions, square the length factor: 1 cm² = 10⁻⁴ m².

Standards and traceability

A measurement standard provides a reference for assigning values. Calibration establishes a relationship between reference values and indications with uncertainty. Traceability requires a documented chain of calibrations, each contributing uncertainty; it is not supplied by using SI notation alone.

Worked example

A capacitor is marked 470 nF and charged to 12 V. C = 470 × 10⁻⁹ F. Charge Q = CV = 5.64 × 10⁻⁶ C = 5.64 μC. Stored energy E = CV²/2 = 33.84 × 10⁻⁶ J = 33.84 μJ, assuming an ideal linear capacitor. The charge and energy have different dimensions and cannot be interchanged.

Quick check

1. Convert 2.2 kΩ to Ω. 2200 Ω.
2. Convert 3 mA to A. 0.003 A.
3. Is kW a unit of energy? No, it is power.