A) \[200\,\Omega \]
B) \[100\,\Omega \]
C) \[300\,\Omega \]
D) \[500\,\Omega \]
Correct Answer: D
Solution :
(d) \[500\,\Omega \] Here, \[L=1\,H,\,C=20\,\mu F=20\times {{10}^{-6}}F\] \[R=300\,\Omega ,\,V=\frac{50}{\pi }Hz\] The inductive reactance is \[{{X}_{L}}=2\pi vL=2\times \pi \times \frac{50}{\pi }\times 1=100\,\Omega \] The capacitive reactance is \[{{X}_{C}}=\frac{1}{2\pi vC}=\frac{1}{2\times \pi \times \frac{50}{\pi }\times 20\times {{10}^{-6}}}=500\,\Omega \] The impedance of the series LCR circuit is \[Z=\sqrt{{{R}^{2}}+{{\left( {{X}_{C}}-{{X}_{L}} \right)}^{2}}}\] \[=\sqrt{{{(300)}^{2}}+{{(500-100)}^{2}}}\] \[=\sqrt{{{(300)}^{2}}+{{(400)}^{2}}}=500\,\Omega \]
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