Relay Coil Formulas: Current and Resistor
Relay coil formulas: coil current and resistance, series resistor for a higher supply, resistor power and coil resistance at temperature.
The formulas
| To find | Formula |
|---|---|
| Coil current | I = P / V |
| Coil resistance | R = V² / P |
| Series resistor for supply Vs | Rs = (Vs − V) / I |
| Resistor power | PR = I² × Rs |
| Coil resistance at temperature | R(t) = R20 × (1 + 0.00393 × (t − 20)) |
V is the rated coil voltage, P the rated coil power from the data sheet and I the rated coil current. A coil on a higher supply with a series resistor works, but the voltage across the coil then changes with the supply and with the coil resistance. The relay must pull in at the lowest supply voltage and not overheat at the highest. A better choice is a relay with the right coil voltage, or a DC-DC converter. The temperature coefficient is that of copper, 0.00393 per °C.
Worked example: a 12 V, 400 mW coil on 24 V
- I = 0.4 / 12 = 33.33 mA and R = 12² / 0.4 = 360 Ω
- Rs = (24 − 12) / 0.03333 = 360 Ω
- PR = 0.03333² × 360 = 0.4 W, so use a resistor of at least twice that rating
Worked example: coil resistance when hot
The same coil at 70 °C.
- R(70) = 360 × (1 + 0.00393 × 50) = 430.7 Ω
- The current at 12 V falls to 27.86 mA
Series resistor for a 12 V, 400 mW coil
| Supply | Series resistor | Resistor power |
|---|---|---|
| 18 V | 180 Ω | 0.2 W |
| 24 V | 360 Ω | 0.4 W |
| 36 V | 720 Ω | 0.8 W |
| 48 V | 1,080 Ω | 1.2 W |
Frequently asked questions
Why does the coil need less current to hold than to pull in?
The air gap is closed when the relay is held, so a smaller magnetic force is enough. Some relays use this to cut the coil power after pull-in.
Why add a diode across a DC relay coil?
When the current stops, the inductance of the coil produces a high voltage spike. A diode across the coil (flyback diode) carries the current and protects the driver.
What happens to the pull-in voltage when the coil is hot?
The resistance rises, so the current for a given voltage falls. The pull-in voltage rises, and the data sheet gives it at a stated temperature.
Can I use a resistor for a 24 V supply?
It works but it wastes power and the coil voltage depends on the supply. Check the pull-in at the lowest supply and the coil power at the highest.
Related
Ohm’s Law FormulasResistor FormulasInductor FormulasElectronics and instrumentation calculatorsThree-Phase Power FormulasPower Factor and the Power TriangleAC Circuit Formulas: Reactance and ImpedanceVoltage Drop Formulas for CablesTransformer Formulas: Current and Fault LevelInduction Motor FormulasLighting Formulas: Lux, Lumens and CandelaBattery Formulas: Capacity and RuntimeSolar PV Formulas: Array Size and StringsCapacitor Formulas: Energy and RC Time ConstantEarthing Formulas: Earth Rod and Fault LoopCable Size Formulas: Current and Short-CircuitEnergy and Cost Formulas: kWh and PaybackGenerator Formulas: kVA, Current and FuelUPS Formulas: kVA, DC Current and BatteryHarmonics Formulas: THD and True Power FactorShort-Circuit Formulas: Fault Level by MVAUnbalance Formulas: Voltage and Neutral CurrentMotor Starting Formulas: DOL, Star-DeltaCircuit Breaker Formulas: Rating and TripCooling Formulas: Airflow and Heat LoadHeating Formulas: Energy and Heater PowerPer-Unit Formulas: Base Values and ImpedanceLED Formulas: Resistor Value and PowerConduit Fill Formulas: Percent Fill and SizeLightning Protection Formulas: Rolling SphereTransformer Efficiency and Regulation FormulasPump Formulas: Hydraulic, Shaft and Motor PowerFan Formulas: Air Power and Affinity LawsRMS, Peak and Average Value FormulasResonance Formulas: Frequency, Q, BandwidthMotor Efficiency Formulas: Input and SavingsDemand, Load and Diversity Factor FormulasCable Tray Fill Formulas: Area and Cable CountConductor Resistance Formulas and TemperatureTransmission Line Formulas: Drop and LossesStar-Delta Conversion Formulas for Resistors4-20 mA Loop Formulas: Scaling and ResistorCable Loss Formulas: Power and Annual CostOp-Amp Formulas: Inverting and Non-Inverting555 Timer Formulas: Frequency and Duty CycleThévenin and Norton FormulasWheatstone Bridge Formulas: Balance and OutputConductor Force Formulas: Short-Circuit ForcesCT Burden Formulas: Lead Resistance and VAGear and Belt Drive Formulas: Speed and TorqueSkin Effect Formulas: Skin DepthRC Filter Formulas: Cutoff Frequency and GainRectifier Ripple Formulas: Capacitor FilterBuck and Boost Converter Formulas: Duty CycleHeat Sink Formulas: Junction TemperatureBattery Pack Formulas: Series and ParallelMotor Acceleration Time FormulasZener Regulator Formulas: Series ResistorBJT Bias Formulas: Voltage Divider BiasPt100 RTD Formulas: Resistance and TemperatureNTC Thermistor Formulas: Beta EquationFusing Current Formulas: Wire Fuse EstimateFlywheel Formulas: Stored EnergyLinear Regulator Formulas: Power and EfficiencyMOSFET Loss Formulas: Conduction and SwitchingTransformer Inrush Current FormulasBattery Charge Time FormulasWind Turbine Power Formulas: Betz LimitDetuning Reactor Formulas: Capacitor BanksTransformer Tap Changer FormulasCable Pulling Tension FormulasInsulation Resistance Formulas: PI and DARPower Transfer and Power Angle FormulasSolar Panel Temperature Derating FormulasVoltage Change and Flicker FormulasSoft Starter and VFD Sizing FormulasEarth Fault Loop and RCD FormulasBattery Internal Resistance FormulasBusbar Size and Short-Circuit FormulasADC Resolution and Sampling FormulasCapacitor Switching Inrush FormulasCable Charging Current FormulasSolar DC to AC Ratio FormulasMeasurement Uncertainty FormulasParallel Transformer Load Sharing FormulasPeukert Law and Battery Runtime FormulasCapacitor Discharge Time FormulasHydraulic Power and Cylinder Force FormulasThermocouple Voltage FormulasTransformer Vector Group FormulasPower Supply Hold-Up Time FormulasHoist and Lift Power FormulasCompressor Power FormulasRectifier Bridge Sizing FormulasPCB Trace Width and Current FormulasHeat Pump COP FormulasSound Level and dB Addition FormulasDuty Cycle and RMS Load FormulasSupercapacitor Energy FormulasStep and Touch Voltage FormulasContactor Sizing FormulasInverter-Fed Motor Cable FormulasPneumatic Cylinder Force and Air UseBusbar Temperature Rise FormulasMotor Temperature Rise FormulasBattery Storage Round-Trip EfficiencyThermal Time Constant FormulasSolar Charge Controller Sizing FormulasPoint Illuminance FormulasGenerator Droop and Load Sharing FormulasTwo-Wattmeter Method FormulasVFD Braking Resistor FormulasLoad Bank Test FormulasTransformer Cooling Class Rating FormulasEnergy Meter Multiplier FormulasOvercurrent Relay Curve FormulasSingle-Tuned Harmonic Filter FormulasCable Sheath Circulating Current FormulasDifferential Protection Slope FormulasEarth Electrode Spacing FormulasSolar Array Row Spacing FormulasDC Lighting Voltage Drop FormulasTransformer Loss of Life FormulasMotor Start Voltage Dip in the Cable FormulasNeutral Earthing Resistor FormulasCable I²t Withstand Check FormulasMotor Locked-Rotor Code Letter FormulasSynchronous Speed and Pole FormulasBattery C-Rate and Cycle Life FormulasEV Charging Time FormulasConveyor Belt Power FormulasParallel Plate Capacitor FormulasSolenoid and Coil Inductance FormulasPower Factor Correction Payback FormulasTransformer Through-Fault Current FormulasTransformer EMF Equation FormulasDelta-Star Resistor Conversion FormulasCurrent Shunt Resistor FormulasSolar Energy Yield and Degradation FormulasElectrolysis and Faraday’s Law FormulasAGL Series Circuit Load and CCR Sizing FormulasAGL Maximum Fittings on a CCR FormulasAGL Isolating Transformer FormulasAGL CCR Input Power and Energy FormulasAGL Brightness Step FormulasAGL Lamp Life FormulasComplex Number Formulas: Polar and RectangularPhasor Addition Formulas: Sum and DifferencePercentage Error Formulas for MeasurementsTrigonometry Formulas for Electrical EngineersMean and Standard Deviation FormulasQuadratic, Logarithm and Power FormulasPercentage, Ratio and Rounding FormulasProbability, Combinations and Binomial FormulasConversion Centre