A) \[1300\,\,\Omega \]
B) \[900\,\,\Omega \]
C) \[500\,\,\Omega \]
D) \[400\,\,\Omega \]
Correct Answer: C
Solution :
In series RLC circuit, the impedance of the circuit is given by \[Z=\sqrt{{{R}^{2}}+{{({{X}_{L}}-{{X}_{C}})}^{2}}}\] Also, \[{{X}_{L}}=\omega L,\,\,{{X}_{C}}=\frac{1}{\omega C}\] \[\therefore \] \[Z=\sqrt{{{R}^{2}}+{{\left( \omega L-\frac{1}{\omega C} \right)}^{2}}}\] Given, \[R=300\,\Omega ,\,\omega =1000\,\,rad/s,\,L=0.9\,H\], \[C=2.0\,\mu F=2\times {{10}^{-6}}F\] Hence, \[Z=\sqrt{{{(300)}^{2}}+{{\left( 1000\times 0.9-\frac{1}{10000\times 2\times {{10}^{-6}}} \right)}^{2}}}\] \[=\sqrt{90000+{{(900-500)}^{2}}}\] \[=\sqrt{90000+16000}\] \[=\sqrt{250000}\] \[=500\,\,\Omega \]
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