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BHU PMT BHU PMT (Mains) Solved Paper-2006

  • question_answer
    A coil of inductance 8.4 mH and resistance\[6\text{ }\Omega \] is connected to a 12V battery. The current in the coil is 1 A at approximately the time:

    A)  500s                                     

    B)  20s

    C)  35ms                                   

    D)  1ms

    Correct Answer: D

    Solution :

                     The current time (i-c) equation in L-R circuit is given by (growth of current in L-R circuit) \[i={{i}_{0}}(1-{{e}^{-t/{{\tau }_{L}}}})\]                        ...(1) where     \[{{i}_{0}}=\frac{V}{R}=\frac{12}{6}=2A\] and        \[{{\tau }_{L}}=\frac{L}{R}=\frac{8.4\times {{10}^{-3}}}{6}=1.4\times {{10}^{-3}}s\] and         \[i=1A\]                                                (given) Substituting these values in Eq. (1) we get                 \[t=0.97\times {{10}^{-3}}s\] Or           \[t\approx 1\,ms\]


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