A) \[2\times {{10}^{4}}V\]
B) \[1.2\times {{10}^{4}}V\]
C) \[2\times {{10}^{-4}}V\]
D) None of these
Correct Answer: A
Solution :
Amount of magnetic flux linked with inductor is \[\phi =Li\] Now, the emf induced-in the inductor is given by \[e=-\frac{d\phi }{dt}=-\frac{d}{dt}(Li)\] \[=-L\frac{di}{dt}\] or \[|e|=L\frac{di}{dt}\] Here, induced current \[=\frac{V}{R}\] \[=\frac{10}{5}\] \[=2A\] Circuit switches off in 1 millisecond or \[dt=1\times {{10}^{-3}}s\] and \[L=10\,H\] \[\therefore \] Induced emf in inductor is \[|e|=10\times \frac{2}{1\times {{10}^{-3}}}\] \[=2\times {{10}^{4}}V\]
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