In a capacitor start and run motors the function of the running capacitor in series with the auxiliary winding is to

improve power factor
increase overload capacity
reduce fluctuations in torque
to improve torque

The correct answer is D. to improve torque.

A capacitor start and run motor is a type of single-phase induction motor that uses two windings, a main winding and an auxiliary winding. The auxiliary winding is connected to a capacitor, which causes it to be out of phase with the main winding. This creates a rotating magnetic field that causes the motor to start. Once the motor is up to speed, the capacitor is disconnected and the motor runs on the main winding.

The running capacitor in series with the auxiliary winding improves torque by providing a phase shift between the two windings. This phase shift creates a rotating magnetic field that is stronger than the magnetic field created by the main winding alone. This stronger magnetic field provides more torque, which allows the motor to start and run more easily.

The other options are incorrect. Option A is incorrect because the running capacitor does not improve power factor. Option B is incorrect because the running capacitor does not increase overload capacity. Option C is incorrect because the running capacitor does not reduce fluctuations in torque.