**Starting a Single Phase Induction Motor with Capacitor Assistance**

**Introduction**

Single phase induction motors are widely used in various applications, including household appliances, industrial machinery, and HVAC systems. However, these motors have a drawback - they are not self-starting. The stator windings of a single phase induction motor do not produce a rotating magnetic field, which is necessary for motor starting. To overcome this limitation, a capacitor is often used to assist in starting the motor. In this article, we will explore the factor that allows a capacitor to help start a single phase induction motor.

**The Role of Capacitor in Motor Starting**

A capacitor is connected in series with the auxiliary winding of the motor, which is also known as the starting winding. The capacitor serves two main purposes:

**1. Phase Shift Creation**

The capacitor creates a phase shift between the current in the main winding and the current in the starting winding. This phase shift is essential for producing a rotating magnetic field, which is necessary for motor starting. The capacitor shifts the phase of the current in the starting winding by 90 degrees with respect to the main winding, resulting in a rotating magnetic field.

**2. Voltage Boost**

The capacitor also provides a voltage boost to the starting winding, which helps to increase the torque produced by the motor during starting. The capacitor acts as a voltage multiplier, increasing the voltage across the starting winding and resulting in a higher torque output.

**The Factor that Allows Capacitor Assistance**

So, what is the factor that allows a capacitor to help start a single phase induction motor? The answer lies in the **capacitive reactance** of the capacitor.

The capacitive reactance (Xc) of a capacitor is inversely proportional to the frequency of the supply voltage and the capacitance value. In a single phase induction motor, the capacitive reactance of the capacitor is used to create a phase shift between the current in the main winding and the current in the starting winding.

**Mathematical Representation**

The capacitive reactance (Xc) of a capacitor can be mathematically represented as:

**Xc = 1 / (2 * π * f * C)**

where:

- Xc is the capacitive reactance in ohms (Ω)
- f is the frequency of the supply voltage in hertz (Hz)
- C is the capacitance value in farads (F)

**Conclusion**

In conclusion, the factor that allows a capacitor to help start a single phase induction motor is the capacitive reactance of the capacitor. By creating a phase shift and providing a voltage boost, the capacitor enables the motor to produce a rotating magnetic field, which is necessary for motor starting. The capacitive reactance of the capacitor is the key to successful motor starting, making it an essential component in single phase induction motor applications.