Why Single-Phase Motors Need Capacitors

A three-phase motor creates a naturally rotating magnetic field from three offset sine waves. A single-phase supply, however, produces only a pulsating field — it doesn't rotate, so a single-phase motor cannot self-start. The capacitor solves this by feeding a second winding (the auxiliary or start winding) with current that is phase-shifted from the main winding. This creates an approximation of a two-phase rotating field.

The phase shift occurs because a capacitor causes current to lead voltage. In an ideal case, the capacitor shifts the auxiliary winding current by 90° relative to the main winding, producing a true rotating field. In practice, the shift is typically 30°–80° depending on the capacitor value and motor design.

The Reactance Formula (Run Capacitors)

A capacitor's opposition to AC current is called capacitive reactance (X_C), measured in ohms:

Rearranging to solve for capacitance when we know the desired current and voltage:

Since capacitance is in farads and motor capacitors are in microfarads (µF), multiply by 10⁶:

• I = auxiliary winding current (amps). Approximated from FLA, power factor, and efficiency.
• f = supply frequency (60 Hz in North America, 50 Hz internationally).
• V = voltage across the capacitor (supply voltage for PSC motors).

For 60 Hz systems, the constant 2π × 60 = 376.99, which simplifies to the well-known field shortcut: C ≈ 2653 × I / V.

Start Capacitor Theory

Start capacitors are electrolytic type — they provide very high capacitance (88–1000+ µF) in a small package, but are designed for intermittent duty only (typically < 3 seconds per start cycle). They produce a much stronger phase shift and higher starting torque than run capacitors.

Sizing is based on the motor's horsepower, voltage, and locked-rotor amps (LRA). Industry-standard tables derived from NEMA MG-1 motor data establish the µF ranges for each HP/voltage combination. The start capacitor must supply enough reactive current to develop the required locked-rotor torque, typically 150%–350% of full-load torque.

Voltage rating: Start capacitors see voltage spikes as the motor accelerates. The back-EMF generated by the spinning rotor adds to the supply voltage across the start winding. A 230V motor can develop 350V+ across the start capacitor during acceleration, which is why start capacitors for 230V motors are rated at 250V or 330V.

Potential Relay Operation

A potential relay (also called a voltage relay) disconnects the start capacitor once the motor reaches approximately 75% of rated speed. It works by sensing the back-EMF voltage generated by the motor's auxiliary winding:

• Pickup voltage: The relay coil is normally closed (NC). At rest, the coil voltage is below the pickup threshold, so the start capacitor is in the circuit.
• As the motor accelerates, back-EMF rises across the start winding. When it exceeds the relay's pickup voltage, the relay opens, disconnecting the start capacitor.
• Dropout voltage: If the motor stalls or slows significantly, back-EMF drops below the dropout voltage and the relay re-closes, reconnecting the start capacitor for another start attempt.
• Continuous coil rating: While running, the relay coil sees the full back-EMF voltage continuously. The coil must be rated for this voltage without overheating.

Common potential relay types (e.g., 395, 065, 066, 067, 068, 069) are matched to specific compressor back-EMF voltage ranges published by compressor manufacturers.

Safety Considerations

Capacitors store electrical energy and can deliver a dangerous shock even after power is removed. Always discharge a capacitor before handling it. Use a 20,000-ohm 5-watt resistor across the terminals, or a dedicated capacitor discharge tool.

Never exceed the capacitor's voltage rating. An undersized voltage rating leads to dielectric breakdown, capacitor rupture, and potential fire. When in doubt, choose the next higher voltage rating.

This calculator provides sizing guidance based on standard engineering formulas. Always verify results against the motor or compressor manufacturer's specifications. Actual capacitor requirements can vary based on ambient temperature, altitude, and specific motor design.