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The Colpitts oscillator has positive feedback where the emitter signal is fed back to the base through C1 which causes some phase shift. The basic idea here is that the positive feedback is adequate to cause the transistor to begin conducting current. As this takes place, C1 and C2 begin to charge. This charge develops a voltage across the capacitors. This voltage is in turn across the inductor L1 which causes the inductor to conduct, building a magnetic field in which the charge is stored and discharging the capacitors. With the capacitors discharging, the inductor can no longer sustain the magnetic field. The field begins to collapse causing a voltage to develop across the capacitors. This cycle of the Capacitors charging and discharging, and the Inductor's magnetic field building and collapsing creates the oscillations of the circuit. Any losses in the oscillations are replenished by current through the transistor.