The type of single-phase induction motor, expected to have the maximum power factor during steady state running condition, is

The correct option is capacitor start, capacitor run.

Detailed Explanation:
Single-phase induction motors are not self-starting and require an auxiliary winding along with a phase-shifting device to create a rotating magnetic field. The performance and power factor of these motors during steady-state running conditions depend on the design and components connected during operation.

Let us analyze the behavior of the given types of motors during steady-state running conditions:

1. Split-phase (resistance start) motor:
In this motor, the auxiliary winding is designed with high resistance and low reactance, while the main winding has low resistance and high reactance. A centrifugal switch disconnects the auxiliary winding once the motor reaches about 75% to 80% of its synchronous speed. During steady-state running, only the main winding (which is highly inductive) is connected to the supply. Consequently, the motor operates with a lagging and relatively low power factor.

2. Capacitor-start motor:
This motor uses an electrolytic capacitor in series with the auxiliary winding to obtain a large phase angle during starting, which provides high starting torque. Similar to the split-phase motor, a centrifugal switch disconnects the starting capacitor and the auxiliary winding once the motor speeds up. During steady-state running, only the main inductive winding remains in the circuit, resulting in a low power factor comparable to the split-phase motor.

3. Shaded-pole motor:
This motor uses shading coils (copper rings) on a portion of each pole to produce a shifting magnetic field. It has extremely low efficiency, low starting torque, and operates at a very poor power factor during steady-state running due to its highly inductive construction and continuous losses in the shading coils.

4. Capacitor-start, capacitor-run motor:
This motor utilizes two capacitors: a larger capacitor (starting capacitor) for high starting torque and a smaller capacitor (running capacitor) for running conditions. The starting capacitor is disconnected by a centrifugal switch after starting, but the running capacitor remains in series with the auxiliary winding continuously during steady-state running.
The running capacitor is specifically sized to optimize the phase angle between the current in the main winding and the current in the auxiliary winding. The capacitive reactance of the running capacitor helps counteract the inductive reactance of the motor windings. This phase compensation causes the total line current to be more in phase with the supply voltage, significantly improving the power factor. As a result, the capacitor-start, capacitor-run motor achieves the maximum power factor among all the options during steady-state running.