Brightness of lamp challenge

The diagram below shows two lamps, A and B, connected in parallel to the mains supply of a house.

A variable resistor is connected at P. State and explain what happens to the brightness of lamp B as the resistance of the variable resistor increases.

Acknowledgement: The diagram is obtained from GEO O-level Physics N11/2/10.

Answer: Brightness of lamp B remains unchanged as the potential difference of the lamp B remains unchanged.