If the centrifugal switch of a single-phase resistance split induction motor does not open after the starting of the motor, the motor will draw high current and get overheated. This is because the centrifugal switch is responsible for disconnecting the starting winding from the circuit once the motor reaches a certain speed. When the switch fails to open, the starting winding remains connected to the circuit, causing an imbalance in the motor's current flow.

Explanation:
1. Centrifugal switch in a split-phase induction motor:
- A single-phase resistance split induction motor typically consists of a starting winding and a main winding.
- The starting winding is used to create a rotating magnetic field during the starting phase of the motor.
- The centrifugal switch is a mechanical device connected to the motor shaft and is designed to open or close the circuit of the starting winding based on the motor's speed.

2. Function of the centrifugal switch:
- During motor starting, the centrifugal switch is closed, allowing current to flow through the starting winding.
- As the motor accelerates, the centrifugal force caused by the rotating shaft pushes the switch contacts outward, eventually opening the circuit of the starting winding.
- This disconnection of the starting winding is crucial for the motor to operate efficiently at the rated speed.

3. Consequences of a failed centrifugal switch:
- If the centrifugal switch fails to open after motor starting, the starting winding remains connected to the circuit even when the motor reaches its rated speed.
- The starting winding, designed for high starting torque but not suitable for continuous operation, continues to draw current.
- This leads to excessive current flow through the motor, causing it to draw high current and get overheated.
- The increased current also puts additional stress on the motor's windings, potentially leading to insulation failure and motor damage.

In conclusion, when the centrifugal switch of a single-phase resistance split induction motor fails to open after the starting of the motor, the motor will draw high current and get overheated due to the continuous connection of the starting winding to the circuit.