A series resonant circuit consists of inductor ' $L$ ' of negligible resistance and a capacitor ' C ' which…

A series resonant circuit consists of inductor ' $L$ ' of negligible resistance and a capacitor ' C ' which produces resonant frequency ' f '. If L is changed to 3 L and ' C ' is changed to 6 C , the resonant frequency will become.
  1. $\frac{\mathrm{f}}{6}$
  2. $\frac{\mathrm{f}}{3}$
  3. $\frac{\mathrm{f}}{2 \sqrt{2}}$
  4. $\frac{\mathrm{f}}{3 \sqrt{2}}$

Solution

Resonant frequency, $f=\frac{1}{2 \pi \sqrt{L C}}$
If L becomes 3 L and C becomes 6 C , then the frequency will become $f^{\prime}=\frac{1}{2 \pi \sqrt{3 L} \cdot 6 \mathrm{C}}=\frac{1}{2 \pi \cdot 3 \sqrt{2} \sqrt{\mathrm{LC}}}=\frac{f}{3 \sqrt{2}}$

Asked in: MHT CET 2024 (10 May Shift 1)

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