In LCR circuit the inductance is changed from L to $9 \mathrm{~L}$. For same resonant frequency the…

In LCR circuit the inductance is changed from L to $9 \mathrm{~L}$. For same resonant frequency the capacitance should be changed from $\mathrm{C}$ to
  1. $9 \mathrm{C}$
  2. $3 \mathrm{C}$
  3. $\frac{C}{9}$
  4. $\frac{C}{3}$

Solution

$\omega=\frac{1}{\sqrt{\mathrm{L}_{1} \mathrm{C}_{1}}}=\frac{1}{\sqrt{\mathrm{L}_{2} \mathrm{C}_{2}}}$ $\therefore \quad \mathrm{L}_{1} \mathrm{C}_{1}=\mathrm{L}_{2} \mathrm{C}_{2}$ $\quad \mathrm{C}_{2}=\frac{\mathrm{L}_{1} \mathrm{C}_{1}}{\mathrm{~L}_{2}}=\frac{\mathrm{L}}{9 \mathrm{~L}} \times \mathrm{C}=\frac{\mathrm{C}}{9}$

Asked in: MHT CET 2020 (15 Oct Shift 1)

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