Why Is the Voltage Across the Terminals of a Permanent Capacitor in a Single-Phase Induction Motor Always Greater Than the Supply Voltage?

The role of a capacitor in a single-phase induction motor is to aid in starting and maintaining the operation of the motor. A capacitor helps the motor initiate due to its energy storage properties and phase shift capabilities, contributing to a higher voltage across the terminals of the capacitor.

The capacitor stores more energy compared to the wire due to its larger surface area, allowing it to hold a greater number of electrons. As these electrons are more distant from the ground, this results in a higher apparent voltage.

How Phase Shift Affects the Voltage

The concept of phase shift is crucial in understanding why the voltage across the capacitor in a single-phase induction motor exceeds the supply voltage. Phase shift is a key factor in the motor's functionality, enabling it to build a rotating magnetic field.

The formula for voltage in a circuit is given by:

V A × Z

Impedance Calculation

Impedance (Z) is a measure that includes the resistance (R) and reactance (X) of the circuit. The reactance due to the auxiliary winding (XL) and the reactance due to the capacitor (XC) contribute to the overall impedance:

Z √(R2 XL2 - XC2)

When XC is greater than XL, the impedance (Z) increases, causing a phase shift that drives the current ahead of the voltage. This is essential for the motor to create a rotating magnetic field.

For optimal performance, we need to ensure:

XC XL

This condition ensures that the impedance (Z) is higher, leading to a greater voltage across the terminals of the capacitor.

To further break down the formula:

V Z × A

A greater impedance (Z) results in a higher voltage (V). This means that the voltage across the capacitor is inherently higher than the supply voltage, due to the phase shift and the nature of the impedance in the circuit.

Resonance in Capacitors and Inductors

There can be situations where a resonance occurs between the capacitor and the inductance of the motor. When resonance happens, energy can build up in the system, potentially leading to significant voltage increases.

Another consideration is the difference between Supply Voltage in RMS (root mean square) and AC peak voltage. The peak voltage is sqrt(2) larger than the RMS voltage:

Vpeak VRMS × √2

This relationship is important to note when measuring and understanding the electrical characteristics of the motor.