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

  • question_answer
    Match the following            Currents                                 r.m.s. values (1)      \[{{x}_{0}}\sin \omega \,t\]     (i)                                            x0 (2)      \[{{x}_{0}}\sin \omega \,t\cos \omega \,t\]          (ii)              \[\frac{{{x}_{0}}}{\sqrt{2}}\] (3)      \[{{x}_{0}}\sin \omega \,t+{{x}_{0}}\cos \omega \,t\]          (iii)           \[\frac{{{x}_{0}}}{(2\sqrt{2})}\]

    A)            1. (i), 2. (ii), 3. (iii)               

    B)            1. (ii), 2. (iii), 3. (i)

    C)            1. (i), 2. (iii), 3. (ii)               

    D)            None of these

    Correct Answer: B

    Solution :

                       1. rms value =\[\frac{{{x}_{0}}}{\sqrt{2}}\]                    2. \[{{x}_{0}}\sin \omega t\cos \omega t=\frac{{{x}_{0}}}{2}\sin 2\omega t\Rightarrow rms\ value =\frac{{{x}_{0}}}{2\sqrt{2}}\]                    3. \[{{x}_{0}}\sin \omega t+{{x}_{0}}\cos \omega t\Rightarrow rms\ value = \sqrt{{{\left( \frac{{{x}_{0}}}{\sqrt{2}} \right)}^{2}}+{{\left( \frac{{{x}_{0}}}{\sqrt{2}} \right)}^{2}}}\]            \[=\sqrt{x_{0}^{2}}={{x}_{0}}\]


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