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A transistor-oscillator using a resonant circuit with an inductor L (of negligible resistance) and a capacitor C in series produce oscillations of frequency f. If L is doubled and C is changed to 4C, the frequency will be

1. 8f
2. f / 2√2
3. f / 2
4. f / 4

Correct answer: f / 2√2

Solution

The frequency of oscillation for an LC circuit is given by f = 1 / (2π√(LC)). If L is doubled and C is changed to 4C, the new frequency becomes f' = 1 / (2π√(2L × 4C)) = 1 / (2π√(8LC)) = f / 2√2.

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