Drawing No. EH–EE–008 // Electrical Engineering
Electrical Engineering Formula Sheet
A practical circuit and power reference from DC fundamentals through AC impedance, three-phase systems and ideal transformer relationships. The equations are suitable for engineering screening; conductor sizing, protection and installation still require the applicable electrical code and equipment standards.
Fast reference, with engineering context
Use the equations directly for screening calculations, then open the linked EngineerHub tools for input handling and unit conversion. Formula applicability and major limitations are stated beside each relation.
Reference conventions
The power triangle
01 // Ohm’s law
For an ohmic element at a stated operating condition, voltage, current and resistance are related linearly.
| Symbol | Meaning | SI units | US customary |
|---|---|---|---|
| V | Voltage | V | V |
| I | Current | A | A |
| R | Resistance | Ω | Ω |
Worked example — 24 V across an 8 Ω load
Given: V = 24 V, R = 8 Ω.
Resistance can change with temperature; nonlinear devices are not described by one constant R.
For AC circuits, Ohm’s law generalizes to phasors: V̲ = I̲Z̲, where impedance can contain resistance and reactance.
02 // Series and parallel resistance
Series resistors carry the same current; parallel resistors have the same voltage.
| Symbol | Meaning | SI units | US customary |
|---|---|---|---|
| Rᵢ | Individual resistance | Ω | Ω |
| Req | Equivalent resistance | Ω | Ω |
Worked example — 4 Ω in series with 6 Ω ∥ 3 Ω
Given: R₁ = 4 Ω; R₂ = 6 Ω; R₃ = 3 Ω.
These relations apply directly to ideal lumped resistors.
Capacitors and inductors combine differently because their impedance depends on frequency. Keep complex phase information for AC networks.
03 // DC / resistive power
Electrical power is the rate of energy transfer. For a resistor, Ohm’s law gives three equivalent forms.
| Symbol | Meaning | SI units | US customary |
|---|---|---|---|
| P | Real power | W | W or hp equivalent |
| V | Voltage | V | V |
| I | Current | A | A |
| R | Resistance | Ω | Ω |
| E | Energy | J, Wh, kWh | Wh, kWh, Btu |
Worked example — 230 V resistive load drawing 10 A
Given: V = 230 V, I = 10 A.
Power and energy are different quantities: kW is a rate; kWh is accumulated energy.
For non-unity-power-factor AC loads, VI is apparent power rather than real power. Use the P–Q–S relations below.
04 // Series RLC impedance
In sinusoidal steady state, a series RLC circuit has resistance plus inductive and capacitive reactance.
| Symbol | Meaning | SI units | US customary |
|---|---|---|---|
| Z | Complex impedance | Ω | Ω |
| R | Resistance | Ω | Ω |
| XL | Inductive reactance | Ω | Ω |
| XC | Capacitive reactance | Ω | Ω |
| f | Frequency | Hz | Hz |
| L | Inductance | H | H |
| C | Capacitance | F | F |
Worked example — series RLC at 50 Hz
Given: R = 20 Ω, L = 50 mH, C = 100 µF, f = 50 Hz, V = 230 V RMS.
A negative phase angle here means the net series load is capacitive.
RMS values are normally used for AC power calculations. Harmonic/non-sinusoidal systems require more than a single-frequency phasor model.
05 // Single-phase AC power triangle
For sinusoidal single-phase systems, real, reactive and apparent power form a right triangle.
| Symbol | Meaning | SI units | US customary |
|---|---|---|---|
| S | Apparent power | VA | VA |
| P | Real power | W | W |
| Q | Reactive power | var | var |
| φ | Voltage-current phase angle | deg or rad | deg or rad |
| PF | Power factor = cosφ | dimensionless | dimensionless |
Worked example — single-phase motor load
Given: V = 230 V, I = 10 A, PF = 0.80 lagging.
Displacement power factor is not the whole story for distorted currents.
For nonlinear loads, true power factor also includes waveform distortion. The simple triangle is exact for sinusoidal steady state.
06 // Balanced three-phase power
For a balanced three-phase load using line-to-line voltage and line current, the √3 relation gives total power.
| Symbol | Meaning | SI units | US customary |
|---|---|---|---|
| VL | Line-to-line RMS voltage | V | V |
| IL | Line RMS current | A | A |
| P | Three-phase real power | W | W |
| Q | Three-phase reactive power | var | var |
| S | Three-phase apparent power | VA | VA |
Worked example — 400 V three-phase load
Given: VL = 400 V, IL = 32 A, PF = 0.90.
The formula assumes a balanced three-phase system.
For wye and delta circuits, line and phase quantities differ. Use the correct line/phase relationships before applying per-phase equations.
07 // Approximate feeder voltage drop
A common balanced three-phase approximation uses the conductor resistance and reactance at operating temperature and frequency.
| Symbol | Meaning | SI units | US customary |
|---|---|---|---|
| I | Line current | A | A |
| L | One-way route length | m | ft |
| R | AC resistance per length, per phase | Ω/m | Ω/ft |
| X | Reactance per length, per phase | Ω/m | Ω/ft |
| φ | Load angle | deg or rad | deg or rad |
| VL | Nominal line voltage | V | V |
Worked example — balanced 400 V feeder
Given: I = 50 A, L = 50 m, R = 0.00050 Ω/m, X = 0.00008 Ω/m, PF = 0.90.
Conductor resistance rises with temperature; use the correct route/loop convention for the chosen formula.
Actual voltage-drop design depends on conductor material, temperature, harmonic content, cable arrangement and applicable electrical-code criteria.
08 // Ideal transformer ratios
For an ideal transformer, voltage ratio equals turns ratio and current ratio is inverse so apparent power is conserved.
| Symbol | Meaning | SI units | US customary |
|---|---|---|---|
| Vp, Vs | Primary / secondary RMS voltage | V | V |
| Np, Ns | Primary / secondary turns | turns | turns |
| Ip, Is | Primary / secondary RMS current | A | A |
Worked example — 400 V to 230 V ideal transformer
Given: Vp = 400 V, Vs = 230 V, Np = 1000 turns, Is = 10 A.
Real transformers have winding resistance, leakage reactance, magnetizing current and core losses.
Use rated kVA, temperature rise, insulation class, impedance and protection requirements for actual transformer selection.
09 // Quick formula summary
Compact print reference. Use the detailed sections above for definitions and limitations.
| Topic | Equation | Purpose | Tool |
|---|---|---|---|
| Ohm | V=IR | DC/resistive relation | Ohm’s law |
| Resistors | Rs=ΣR; 1/Rp=Σ1/R | Equivalent resistance | Series/parallel |
| Power | P=VI | Power and energy | Electrical power |
| RLC | Z=R+j(XL−XC) | AC current and phase | Circuit load |
| AC P-Q-S | P=VIcosφ | Power factor | Electrical power |
| Three-phase | P=√3VLILcosφ | Balanced 3φ power | Electrical power |
| Voltage drop | ΔV≈√3IL(Rcosφ+Xsinφ) | Feeder screening | Voltage drop |
| Transformer | Vp/Vs=Np/Ns | Ideal ratio | Turns ratio |
10 // Assumptions & limitations
Fundamental equations are only useful when their assumptions match the actual problem.
Unless stated otherwise, AC voltage/current formulas use RMS quantities and sinusoidal steady state. Harmonics require waveform-specific analysis.
This is not a conductor-sizing, protection, grounding or installation code. Use the locally applicable IEC/NEC/national standards and manufacturer data for design.
The compact √3 formulas assume balanced loads. Unbalance requires phase-by-phase analysis.
11 // Technical references
The DOE handbooks are archived fundamentals/training references and are not current installation codes. Use current local electrical standards for design compliance.