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So as opposed to a BJT transistor (which has a large but measurable input impedance) a Mosfet has even larger (presumably infinite) impedance. The reason is because of a small non-conducting zone that exists between the Gate side and the Drain-Source side. It acts as a small capacitor (which capacitors have infinite resistance), and the electromagnet field produced is what drives current between Source and Drain. Now, why is this desirable? In the case of BJT's there is a small current that flows into the base, essentially drawing small but existent power from the circuit connected at the Base. It is more ideal to have a transistor that completely separates the current of the control circuit and the current in the circuit being switched/supplied. Simply, it means its more efficient. When BJT transistors are turned off, power is still being used. The same isn't necessarily true for Mosfet transistors.

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Q: Why input impedance of mosfet is high?
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