Electrical quantities are expressed in SI units: the volt for potential difference, the ampere for current, the ohm for resistance, the watt for power and the coulomb for charge. Decimal prefixes scale these units by powers of ten.
Learning objectives
- Name the SI units for voltage, current, resistance, power and charge.
- Relate derived units such as the volt, ohm and watt to base units.
- Convert values between milli, base, kilo and mega prefixes.
- Avoid common prefix and notation errors in calculations.
Progressive explanation
Start with the plain-language idea, then move into the engineering detail. Each level stands on its own, so you can stop at the depth you need.
Beginner The core idea
For example, 0.022 A is written 22 mA, 4,700 Ω is written 4.7 kΩ, and 1,500 W is written 1.5 kW. Reading these prefixes correctly is essential: confusing m (milli, 10⁻³) with M (mega, 10⁶) changes a value by a factor of a billion.
Intermediate How it behaves in a circuit
Unit conversion is part of every calculation. A current of 250 mA is 0.250 A; a resistance of 4.7 kΩ is 4,700 Ω. Combining milliampères and kilo-ohms is convenient because 1 mA × 1 kΩ = 1 V, which is why the V = I × R triangle works directly with mA and kΩ to give volts.
Advanced Limits, assumptions, engineering detail
Notation also matters: the SI rule is a space between the number and the unit symbol (12 V, not 12V), and unit symbols are case-sensitive (m for milli, M for mega; S for siemens, s for second). Prefixes should not be combined, so picofarads are written pF, not μμF. In data sheets, mixed prefixes are common, so converting everything to base units before calculating avoids order-of-magnitude errors.
Formulas and variables
Units of measurement
| Quantity | Symbol | Unit |
|---|---|---|
| Voltage | V | volt (V) |
| Current | I | ampere (A) |
| Resistance | R | ohm (Ω) |
| Power | P | watt (W) |
| Charge | Q | coulomb (C) |
| Capacitance | C | farad (F) |
Worked examples
Converting resistance
Problem. A resistor is marked 4.7 kΩ. What is its resistance in ohms?
Solution. kilo means 10³, so 4.7 kΩ = 4.7 × 1,000 Ω = 4,700 Ω.
Converting current and using Ohm’s law
Problem. A 3.3 kΩ resistor has 5.0 V across it. Find the current in milliamperes.
Solution. I = V/R = 5.0 V / 3,300 Ω = 0.001515 A. Multiply by 1,000: I ≈ 1.52 mA. Using mA and kΩ directly: I = 5.0 / 3.3 ≈ 1.52 mA.
Practical applications
- Reading component markings and datasheets
- Configuring multimeter ranges
- Checking power and energy consumption
- Converting battery capacity units
Automotive applications
Automotive specifications mix units: battery capacity in amp-hours, fuses in amperes, cable sections in square millimetres, power in watts or kilowatts, and sensor signals in millivolts or volts. Converting everything to base units before calculating prevents mistakes, especially when a specification gives milliamperes for a parasitic drain and amperes for a charging current.
Industrial applications
Industrial nameplates use kilowatts for motor output, amperes for rated current, volts for supply, and kilovolt-amperes for apparent power. Energy billing uses kilowatt-hours, a unit of energy, not power. Understanding the distinction between kW and kWh is essential when estimating consumption or comparing equipment.
Measurement procedure
- Check the prefix on the meter display and on the component or specification before recording a value.
- Note that some instruments show m for milli and M for mega with different case, which is easy to misread.
- Use the base unit in written work; convert back to a convenient prefix only for the final answer.
- Include the unit with every number; a value without a unit is ambiguous in electrical work.
Common mistakes
- Confusing m (milli, 10⁻³) with M (mega, 10⁶), a factor of 10⁹ difference.
- Treating kWh as a unit of power; it is a unit of energy, equal to one kilowatt for one hour.
- Mixing prefixes in a formula without converting, for example using mA with MΩ and expecting volts.
- Writing unit symbols without a space or with the wrong case, such as 12v instead of 12 V.
Safety considerations
- A prefix error can turn a safe low voltage into a dangerous high voltage in a calculation; always check the order of magnitude.
- Do not assume a component can handle a value because the number looks small; read the unit and the rating.
- When selecting a meter range, start with the highest range and reduce it to avoid overrange damage.