question_answer

As given in the figure, a series circuit connected across a 200 V, 60 Hz line consists of a capacitor of capacitive reactance \[30\,\,\Omega \], a non-inductive resistor of \[44\,\,\Omega \]. and a coil of inductive reactance \[90\,\,\Omega \]. and resistance\[36\,\,\Omega \]. The power dissipate in the coil is  

A)  320 W                  

B)  176 W

C)  144 W                  

D)  0

Correct Answer: A

Solution :

                                We have, \[{{X}_{L}}=90\,\Omega ,\,{{X}_{C}}=30\,\Omega \]                 and        \[R={{R}_{1}}+{{R}_{2}}=44+36=80\,\Omega \] Impedance \[Z=\sqrt{{{R}^{2}}+{{({{X}_{L}}-{{X}_{C}})}^{2}}}\]                 \[=\sqrt{{{(80)}^{2}}+{{(60)}^{2}}}\]                 \[Z=\sqrt{6400+3600}=100\]                 \[I=\frac{V}{Z}=\frac{200}{100}=2A\]                 \[{{P}_{av}}={{I}^{2}}R\]                 \[={{(2)}^{2}}\times 80=320\,\,W\]