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:
- (b) We know that frequency of electrical oscillation in L.C. circuit is
$f=\frac{1}{2 \pi} \sqrt{\frac{1}{L C}}$
Now, $L=2 L & C=4 C$
$f^{\prime}=\frac{1}{2 \pi} \sqrt{\frac{1}{2 L .4 C}}=\frac{1}{2 \pi} \sqrt{\frac{1}{L C}} \times \frac{1}{2 \sqrt{2}}$
$\Rightarrow f^{\prime}=\frac{1}{2 \sqrt{2}} \times f$
