A) \[{{i}_{1}}={{i}_{2}}\] and \[{{i}_{1}}>{{i}_{3}}\]
B) \[{{i}_{1}}={{i}_{2}}\] and \[{{i}_{1}}<{{i}_{3}}\]
C) \[{{i}_{1}}={{i}_{2}}\]and \[{{i}_{2}}={{i}_{3}}\]
D) \[{{i}_{1}}={{i}_{2}}\]and \[{{i}_{3}}=0\]
Correct Answer: B
Solution :
At resonance \[{{i}_{3}}=\frac{200}{80}\,=2.5A\] \[{{X}_{L}}={{X}_{C}}\,=\omega L\,=\sqrt{\frac{L}{C}}\,(As\,\omega =\frac{1}{\sqrt{LC}}\,)\] \[=\sqrt{\frac{10}{160\,\times {{10}^{-6}}}}=250\Omega \] \[{{i}_{1}}={{i}_{2}}\] and \[{{i}_{1}}<{{i}_{3}}\]
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