1. Tardigrade
  2. Question
  3. Physics
  4. The inductance L (in mH) of the coil which is to be connected in series with a capacitor of 0.3 pF to get an oscillatory frequency of 1 MHz is:

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The inductance L (in mH) of the coil which is to be connected in series with a capacitor of 0.3 pF to get an oscillatory frequency of 1 MHz is:

EAMCETEAMCET 2005Alternating Current

Solution:

The frequency of oscillation of L-C circuit is given by $ f=\frac{1}{2\pi \sqrt{LC}} $ or $ LC=\frac{1}{4{{\pi }^{2}}{{f}^{2}}} $ $ L=\frac{1}{4{{\pi }^{2}}{{f}^{2}}C} $ Here, $ f=1MHz=1\times {{10}^{6}}Hz, $ $ C=0.3pF=0.3\times {{10}^{-12}}F $ $ \therefore $ $ L=\frac{1}{4\times \frac{22}{7}\times \frac{22}{7}\times {{({{10}^{6}})}^{2}}\times 0.3\times {{10}^{-12}}}H $ $ L=\frac{490}{4\times 484\times 3\times {{10}^{12}}\times {{10}^{-12}}}H $ $ L=0.0844\,H $ $ L=874.4\,mH $