A) \[2\,\pi \]
B) \[5\,\pi \]
C) \[\,\pi \]
D) \[4\pi \]
Correct Answer: B
Solution :
Key Idea: For maximum value of emf in the second coil, the rate of change of current \[\left( \frac{dI}{dt} \right)\]should be maximum. The given equation of current changing in the first coil is \[I={{I}_{0}}\sin \omega t\] ...(i) Differentiating Eq. (i) with respect to time, we have \[\frac{dI}{dt}=\frac{d}{dt}({{I}_{0}}\sin \omega t)\] \[or\frac{dI}{dt}={{I}_{0}}\frac{d}{dt}(\sin \omega t)\] \[or\frac{dI}{dt}={{I}_{0}}\omega \,\cos \,\omega t\] For maximum \[\frac{dI}{dt}\], the value of \[\cos \,\omega t\] should be equal to 1. So, \[{{\left( \frac{dI}{dt} \right)}_{\max }}={{I}_{0}}\,\omega \] The maximum value of emf is given by \[\therefore {{e}_{\max }}=M{{\left( \frac{dI}{dt} \right)}_{\max }}=M{{I}_{0}}\omega \] Here, \[M=0.005\,H,\,{{I}_{0}}=10\,A,\,\omega =100\pi \,\,rad/s\] \[\therefore {{e}_{\max }}=0.005\times 10\times 100\pi =5\pi \]
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