I have the following circuit schema. The engine is not spinning, but if I replace it with a led, the led shines. Could anybody give me an explanation and how to fix it? Thank you.
The engine spins if I directly use the 3v source.
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In your original circuit, you are using the transistor to create a short circuit around the LED or motor - this would be very wasteful if the collector resistor could pass enough current to allow the motor to operate.
(By the way, in English, "engine" usually means something like a car engine, running on petrol/gasoline or diesel. You are talking about an electric motor.)
The preferred circuit to operate a motor is something like:
When V1 is 3 volts, the transistor will conduct, turning the motor on. If V1 is zero volts, the transistor will be turned off, and the motor will stop.
Edits suggested by comments:
D1 is a "flyback diode" to suppress voltage spikes when the motor is turned off. The transistor must be rated to carry the motor current.
LED D2, and a current-limiting resistor should be connected as shown (with or without the motor).