KVPY Sample Paper KVPY Stream-SX Model Paper-23

The magnetic flux \[\phi \] through a metal ring varies with time t according to: \[\phi =3\,(a{{t}^{3}}-b{{t}^{2}})T{{m}^{2}},\] with \[a=2{{s}^{-\,3}}\]and \[b=6\,{{s}^{-\,2}}.\] The resistance of the ring is \[3\,\Omega \,.\]The maximum current induced in the ring during the interval \[t=0\] to \[t=2s,\] is

A) 1 A

B) 2 A

C) 3 A

D) 6 A

Correct Answer: D

Solution :

i. (t) \[=-\frac{1}{R}\frac{d\phi }{dt}=2bt-3a{{t}^{2}}\]

i is maximum when \[\frac{di}{dt}=0\] or \[t=\frac{2b}{6a}\]

Using values, at \[t=1\,\,\text{s},\]i is maximum its value \[=12-6=6A\]