Explanation:
\({\omega _0} = 2\pi n\)
\({\omega _0} = 2 \times 3 \times 100 = 600rad/s\) (\(\because \) \(\pi = 3\))
Further \({\omega _0} = \frac{1}{{\sqrt {LC} }}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\)
Also,
\({X_C} = \frac{1}{{{\omega _0}C}} = 60\Omega \Rightarrow C = \frac{1}{{{\omega _0} \times 60}} = \frac{1}{{600 \times 60}}\)
\( \Rightarrow C = \frac{1}{{36 \times {{10}^3}}}F\)
So, put values in eq. (1), we get
\(600 = \frac{1}{{\sqrt {L\left( {\frac{1}{{36 \times {{10}^3}}}} \right)} }} \Rightarrow 36 \times {10^4} = \frac{{36 \times {{10}^3}}}{L}\)
\(\therefore \quad L = \frac{{36 \times {{10}^3}}}{{36 \times {{10}^4}}} = \frac{1}{{10}} = 0.1H\)