Question

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:

• A. 8.44
• B. 84.4
• C. 844
• D. 8440

Answer 1

Answer: (B)

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, $f=1MHz=1\times {10}^{6}Hz,$ $C=0.3pF=0.3\times {10}^{-12}F$ $\therefore$ $L=\frac{1}{4\times \frac{22}{7}\times \frac{22}{7}\times {({10}^6)}^2\times 0.3\times {10}^{-12}}H$ $L=\frac{490}{4\times 484\times 3\times {10}^{12}\times {10}^{-12}}H$ $L=0.0844H$ $L=874.4mH$