AkCalculators

Electrical Power — fundamentals, measurement and thermal design

Electrical power is the rate at which electrical energy is transferred or converted. In circuits it quantifies how much work is done (or heat produced) per unit time. Power affects component selection, thermal design, energy billing and safety systems. This article explains the core formulas for power in resistive circuits, measurement techniques, thermal implications, common calculation rearrangements, and practical examples to guide engineering decisions.

What is power?

Power (P) is energy per unit time. In SI units, power is measured in watts (W), where one watt equals one joule per second. In electrical circuits, instantaneous power p(t) = v(t) × i(t) where v(t) and i(t) are instantaneous voltage and current. For steady-state DC or for AC using RMS values (and purely resistive loads), P = V_rms × I_rms gives the average power converted to heat or useful work.

Core relations for resistive circuits

For resistive loads, the fundamental relations are:

• P = V × I
• P = I² × R
• P = V² / R

These forms allow solving for any one quantity when two are known. For AC circuits with reactance, use RMS values and impedance (Z) and separate real power (P) from reactive power (Q) where necessary.

Measurement techniques

Measure power directly with power meters or indirectly by measuring voltage and current separately and multiplying (V × I). For AC systems, true-RMS meters or power analyzers are required to account for waveform distortion. In three-phase systems, use appropriate three-phase power meters or calculate per-phase values and combine them properly depending on star/delta configuration.

Thermal design and derating

Power dissipated in resistive elements becomes heat. Thermal management—through heatsinks, airflow, PCB copper area, and component selection—is critical. Components should be derated (chosen with higher power ratings than expected dissipation) to increase reliability. Manufacturers provide thermal resistance and derating curves for components such as resistors and semiconductors—use these to determine safe operating conditions.

Units, prefixes and common pitfalls

Use correct unit prefixes: 1 W, 1 kW = 1000 W, 1 mW = 0.001 W. Be careful converting milliamps to amps and millivolts to volts when computing power, since small conversion errors cause large mistakes in power calculation. For AC motors and inductive loads, consider apparent power (VA) and power factor; billing often depends on real power (kW) and sometimes on reactive power (kVAr).

AC, power factor and phasors

In AC circuits with non-unity power factor, apparent power S = V_rms × I_rms, real power P = S × cos(φ) where cos(φ) is the power factor, and reactive power Q = S × sin(φ). For resistive loads cos(φ) ≈ 1 and P ≈ S. For full analyses of AC circuits, phasor arithmetic and complex power are required.

Worked examples

Example 1 — DC resistive load: A 12 V supply drives 2 A through a resistor. P = V × I = 12 × 2 = 24 W. Equivalent R = V / I = 6 Ω.

Example 2 — From current and resistance: A system carries 0.5 A through a 100 Ω resistor. P = I² × R = 0.5² × 100 = 25 W. Voltage across the resistor = V = I × R = 50 V.

Example 3 — From voltage and resistance: A resistor sees 10 V across it and has resistance 20 Ω. P = V² / R = 100 / 20 = 5 W.

Safety and protective devices

Design protection (fuses, circuit breakers, thermal cutouts) around worst-case power and short-circuit scenarios. For power electronics, include snubbers and soft-start/current-limiting features to manage inrush and switching losses. Ensure wiring and connectors are sized for expected continuous and peak power conditions.

Using this calculator effectively

Enter any two independent values among V, I and R. Leave the Power field blank to compute it directly — or leave any fields blank and the solver will derive unknown quantities. Enable step-by-step derivation for documentation or learning. Use the precision selector to format outputs for reports and enable CSV export for lab logs.

Power calculations are simple algebraically but fundamental to safe, reliable electrical design. Combine careful measurement with conservative thermal design and appropriate protection to ensure systems operate safely and efficiently.