A) \[10\,\,V\]
B) \[30\,\,V\]
C) \[45\,\,V\]
D) \[90\,\,V\]
Correct Answer: A
Solution :
Magnetic flux\[\phi =5{{t}^{2}}+3t+16\] Then the induced emf as given by \[E=\frac{d\phi }{dt}=\frac{d}{dt}(5{{t}^{2}}+3t+16)\] \[E=10t+3\] ... (1) When \[t=3\] from above Eq. (1), we get \[{{E}_{3}}=(10\times 3)+3\] \[{{E}_{3}}=33V\] ... (2) When\[t=4\], from Eq. (1), we get \[{{E}_{4}}=10\times 4+3=43V\] ... (3) Hence, emf induced in fourth second is \[={{E}_{4}}-{{E}_{3}}=43-33=10V\] [From Eqs. (2) and (3)]
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