Discussion
What is the resonant frequency of the given oscillator if \(R = 51\ \mathrm{k\Omega}\) and \(C = 0.001\ \mu\mathrm{F}\)?
Answer: B
The circuit is a Wien bridge oscillator: the op-amp with a series RC and a parallel RC arm in the bridge. The frequency at which the bridge is balanced and the feedback has zero phase shift is
\[ \begin{aligned} f = \frac{1}{2\pi R C} \\ &= \frac{1}{2\pi \times 51 \times 10^{3} \times 0.001 \times 10^{-6}} \end{aligned} \]
\[ f = \frac{1}{3.204 \times 10^{-4}} = 3120.7\ \text{Hz} \]
The other values are factors of ten or a hundred away, which would come from a slip in the capacitance, 0.001 microfarad being \(10^{-9}\) F. The answer is 3120.7 Hz, option B.
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