A) \[\frac{5({{\pi }^{2}}-5)}{\pi }\Omega \]
B) \[\frac{{{10}^{2}}(10-{{\pi }^{2}})}{\pi }\,\Omega \]
C) \[\frac{10({{\pi }^{2}}-5)}{\pi }\,\Omega \]
D) \[\frac{{{5}^{2}}(10-{{\pi }^{2}})}{\pi }\Omega \]
Correct Answer: B
Solution :
[b] Here, \[{{X}_{L}}={{\omega }_{L}}=2\pi fL=2\pi \times 50\times 1=100\pi \,\Omega \] \[{{X}_{c}}=\frac{1}{\omega C}=\frac{1}{2\pi fC}=\frac{1}{2\pi \times 50\times 10\times {{10}^{-6}}}=\frac{{{10}^{3}}}{\pi }\Omega \] So, \[=\left| {{X}_{L}}-\left. {{X}_{C}} \right| \right.=\left| 100\pi -\left. \frac{{{10}^{3}}}{\pi } \right| \right.=\left| {{10}^{2}}\left. \left[ \frac{{{\pi }^{2}}-10}{\pi } \right] \right| \right.\Omega \]
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