Alternating Current: Practice Problem & Solution
30. 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: (2006)
Solution Explained:
To solve this problem, we apply the core principles of Alternating Current. Understanding the underlying formula is key to arriving at the correct answer below:
The frequency of oscillation for an LC circuit is $f = \frac{1}{2\pi\sqrt{LC}}$.
When the inductance is doubled ($L' = 2L$) and capacitance is quadrupled ($C' = 4C$), the new frequency is $f'$.
$f' = \frac{1}{2\pi\sqrt{(2L)(4C)}} = \frac{1}{2\pi\sqrt{8LC}} = \frac{1}{\sqrt{8}} \cdot \frac{1}{2\pi\sqrt{LC}}$.
Thus, the new frequency is $f' = \frac{f}{2\sqrt{2}}$.
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