A) \[100\,\,mH\]
B) \[1\,\,mH\]
C) Cannot be calculated unless R is known
D) \[10\,\,mH\]
Correct Answer: A
Solution :
Key Idea In resonance condition, maximum current flows in the circuit. Current in \[LCR\] series circuit, \[i=\frac{V}{\sqrt{{{R}^{2}}+{{({{X}_{L}}-{{X}_{C}})}^{2}}}}\] where \[V\] is rms value of current, \[R\] is resistance, \[{{X}_{L}}\] is inductive reactance and \[{{X}_{C}}\] is capacitive reactance. For current to be maximum, denominator should be minimum which can be done, if \[{{X}_{L}}={{X}_{C}}\] This happens in resonance state of the circuit\[ie,\] \[\omega L=\frac{1}{\omega C}\] or \[L=\frac{1}{{{\omega }^{2}}C}\] Given,\[\omega =1000\,\,{{s}^{-1}},\,\,C=10\mu F=10\times {{10}^{-6}}F\] Hence, \[L=\frac{1}{{{(1000)}^{2}}\times 10\times {{10}^{-6}}}\] \[=0.1H\] \[=100\,\,mH\]
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