a relay works by having an electromagnetically actuated switch.
the voltage across the POWER + and – connections is controlled by having voltage across the SIGNAL + and – connections.
a mosfet works in more or less the same way. the RESISTANCE of the connection between the Source (S) and Drain (D) connections on the MOSFET is controlled by the voltage difference between the GATE (G) and Body (B) connections.
just as your relay can be Normally Open (signal turns the relay off) or Normally closed (signal turns the relay ON), MOSFETS can also be normally open (P channel) or normally closed (N channel)
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