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JEE Main & Advanced Physics Alternating Current / प्रत्यावर्ती धारा Question Bank Critical Thinking

  • question_answer
    An LCR series circuit with a resistance of 100 ohm is connected to an ac source of 200 V (r.m.s.) and angular frequency 300 rad/s. When only the capacitor is removed, the current lags behind the voltage by \[{{60}^{o}}\]. When only the inductor is removed the current leads the voltage by \[{{60}^{o}}\]. The average power dissipated is 

    A)            50 W                                        

    B)            100 W

    C)            200 W                                      

    D)            400 W

    Correct Answer: D

    Solution :

                       \[\tan \varphi =\frac{{{X}_{L}}}{R}=\frac{{{X}_{C}}}{R}\Rightarrow \tan {{60}^{o}}=\frac{{{X}_{L}}}{R}=\frac{{{X}_{C}}}{R}\]                    \[\Rightarrow {{X}_{L}}={{X}_{C}}=\sqrt{3}\ R\]                    i.e. \[Z=\sqrt{{{R}^{2}}+{{({{X}_{L}}-{{X}_{C}})}^{2}}}=R\]            So average power \[P=\frac{{{V}^{2}}}{R}=\frac{200\times 200}{100}\]= 400W


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