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
- $9 \mathrm{C}$
- $3 \mathrm{C}$
- $\frac{C}{9}$
- $\frac{C}{3}$
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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