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GATE ECE 2015 Set 2 | Question: 30

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An $LC$ tank circuit consists of an ideal capacitor $C$ connected in parallel with a coil of inductance $L$ having an internal resistance $R.$ The resonant frequency of the tank circuit is

  1. $\dfrac{1}{2\pi \sqrt{LC}}$
  2. $\dfrac{1}{2\pi \sqrt{LC}}\sqrt{1-R^{2}\dfrac{C}{L}}$
  3. $\dfrac{1}{2\pi \sqrt{LC}}\sqrt{1- \dfrac{L}{R^{2}C}}$
  4. $\dfrac{1}{2\pi \sqrt{LC}}\left(1-R^{2}\dfrac{C}{L}\right)$

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