A) \[\frac{aT}{3R}\]
B) \[\frac{{{a}^{2}}{{T}^{2}}}{3R}\]
C) \[\frac{{{a}^{2}}{{T}^{2}}}{R}\]
D) \[\frac{{{a}^{2}}{{T}^{3}}}{3R}\]
Correct Answer: D
Solution :
[d] Given that \[\phi =at(T-t)\] Induced emf, \[E=\frac{d\phi }{dt}=\frac{d}{dt}[at(T-t)]\] = at \[(0-1)+a(T-t)=a(T-2t)\] So, induced emf is also a function of time. \[\therefore \] Heat generated in time T is \[H\int\limits_{0}^{T}{\frac{{{E}^{2}}}{R}}dt=\frac{{{a}^{2}}}{R}\int\limits_{0}^{T}{{{(T-2t)}^{2}}}\] \[dt=\frac{{{a}^{2}}{{T}^{3}}}{3R}\]You need to login to perform this action.
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