Search any question & find its solution
Question:
Answered & Verified by Expert
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
Options:
frequency the capacitance should be changed from $\mathrm{C}$ to
Solution:
1005 Upvotes
Verified Answer
The correct answer is:
$\frac{C}{9}$
$\omega=\frac{1}{\sqrt{\mathrm{L}_{1} \mathrm{C}_{1}}}=\frac{1}{\sqrt{\mathrm{L}_{2} \mathrm{C}_{2}}}$
$\therefore \quad \mathrm{L}_{1} \mathrm{C}_{1}=\mathrm{L}_{2} \mathrm{C}_{2}$
$\quad \mathrm{C}_{2}=\frac{\mathrm{L}_{1} \mathrm{C}_{1}}{\mathrm{~L}_{2}}=\frac{\mathrm{L}}{9 \mathrm{~L}} \times \mathrm{C}=\frac{\mathrm{C}}{9}$
$\therefore \quad \mathrm{L}_{1} \mathrm{C}_{1}=\mathrm{L}_{2} \mathrm{C}_{2}$
$\quad \mathrm{C}_{2}=\frac{\mathrm{L}_{1} \mathrm{C}_{1}}{\mathrm{~L}_{2}}=\frac{\mathrm{L}}{9 \mathrm{~L}} \times \mathrm{C}=\frac{\mathrm{C}}{9}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.