Final answer:
The float-controlled valve used in a water closet is called a ballcock valve (option b). It uses a float mechanism to regulate the water level in the tank, refilling it after a flush and stopping the flow once full.
Step-by-step explanation:
The float-controlled valve used in a water closet is also referred to as a ballcock valve. This type of valve is instrumental in regulating the flow of water into the tank after it has been flushed. The operation of a ballcock valve involves a float mechanism that rises and falls with the water level, triggering the valve to refill the tank after a flush or to stop the water flow once the tank is full.
Considering the reference to flow-through in ballast tanks, this principle, although similar in maintaining levels, is distinct in application from the water closet ballcock valve. For a ballast tank, water is typically drawn in through a lower valve and expelled through an upper opening, ensuring the tank is flushed with a volume up to 300% of its capacity to maintain proper balance and stability of a vessel. The ballcock valve is specifically designed for a controlled and cyclical refilling of water closets.