Discussion
The frequency of the following Hartley oscillator
is nearly equal to :
Answer: B
The frequency is nearly 159 kHz.
In a Hartley oscillator the tank circuit is a capacitor across two inductors in series, so (neglecting mutual inductance) \(L = L_{1} + L_{2}\):
\[ \begin{aligned} L &= 12 + 8 = 20\ \mu\text{H} \\ LC &= 20 \times 10^{-6} \times 0.05 \times 10^{-6} = 10^{-12} \\ f &= \frac{1}{2\pi\sqrt{LC}} = \frac{1}{2\pi \times 10^{-6}} \\ &\approx 159\ \text{kHz} \end{aligned} \]
Using only the 12 \(\mu\)H coil gives about 205 kHz, and only the 8 \(\mu\)H coil about 252 kHz; neither is an option. 139, 179 and 279 kHz do not follow from these component values.
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