A) \[1.25\times {{10}^{-8}}H\]
B) \[3.07\,\times {{10}^{-8}}\,H\]
C) \[2.25\,\times {{10}^{-8}}\,H\]
D) \[1.9\,\times {{10}^{-8}}H\]
Correct Answer: B
Solution :
Given: \[\lambda =360m,\,C=1.20\,\mu F=1.2\times {{10}^{-6}}F\] The frequency of radio waves transmitted from the transmitting station is \[f=\frac{c}{\lambda }=\frac{3\times {{10}^{8}}}{360}=8.3\times {{10}^{5}}\,Hz\] Frequency of series resonant circuit is given by\[f=\frac{1}{2\pi \sqrt{LC}}\] \[\therefore \] \[L=\frac{1}{{{(2\pi f)}^{2}}C}\] \[=\frac{1}{{{(2\times 3.14\times 8.3\times {{10}^{5}})}^{2}}\times 1.2\times {{10}^{-6}}}\] \[=3.07\times {{10}^{-8}}H\]
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