Alternating Current - Result Question 39

41. 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 $4 C$, the frequency will be

[2006]

(a) $8 f$

(b) $f / 2 \sqrt{2}$

(c) $f / 2$

(d) $f / 4$

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Answer:

Correct Answer: 41. (b)

Solution:

  1. (b) We know that frequency of electrical oscillation in L.C. circuit is

$f=\frac{1}{2 \pi} \sqrt{\frac{1}{L C}}$

Now, $L=2 L & C=4 C$

$f^{\prime}=\frac{1}{2 \pi} \sqrt{\frac{1}{2 L .4 C}}=\frac{1}{2 \pi} \sqrt{\frac{1}{L C}} \times \frac{1}{2 \sqrt{2}}$

$\Rightarrow f^{\prime}=\frac{1}{2 \sqrt{2}} \times f$