Discussion
That Colpitts therefore needs an amplifier gain of at least
Answer: D
The loop gain must reach unity:
\[ A \ge \frac{1}{\beta} = 10 \]
giving 10, with some margin in practice so the circuit starts reliably. The gain requirement is always the reciprocal of the feedback fraction, whatever the topology, which is why computing the fraction first answers the gain question without any further work.
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