Discussion
A Colpitts uses \( L = 100 \ \mathrm{\mu H} \) with \( C_{1} = C_{2} = 1 \ \mathrm{nF} \). Its frequency is about
Answer: A
The two capacitors appear in series across the inductor:
\[ \begin{aligned} C_{s} &= \tfrac{C_{1}C_{2}}{C_{1}+C_{2}} = 0.5 \ \mathrm{nF} \\ f &= \tfrac{1}{2\pi\sqrt{LC_{s}}} \approx 712 \ \mathrm{kHz} \end{aligned} \]
giving about 712 kHz. Using one nanofarad rather than the series combination gives 503 kHz, which is the commonest error. The series rule for capacitors is what makes the Colpitts calculation differ from the Hartley's.
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