Spoken like a Plumber.
Sorry, but with respect I have to disagree....no red X.....
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A relay cannot drop the 'amperage' (not even sure if that's a real word yet). A relay is a device used to divert the 'current' away from the switching mechanism, directly to the load. (fan in this case)
A switch typically is used for switching the relay coil, which consumes a fraction of the current of the of the load being controlled.
A switch can be used for switching the load directly, but the switch contacts must be rated for the appropriate load, and voltage as well as number of operations it will be used to switch the load.
A fuse is the device used to prevent to break the circuit in the case of an overload of current to the load.
The fuse does not control the current flow - it is only there as a safety device to cut the circuit.
Current flow if controlled by either a limiting resistor, or the load itself. However, if the load (fan in this case) becomes compromised by a short circuit, then control is lost, and the current increases dramatically, and rapidly, and this is where the fuse operates.
Electrical work is not easy, and caution should be exercised by those who are not sure of what they are doing. It frightens me sometimes when I see guys installing their own electrical mains supplies and distribution panels at home here.
BTW, I am not the expert, I am sure others will want to add their 5 cents worth. I'm just an ordinary Electrician with 40+ years under my belt.