The magnetic flux linked with a coil (in Wb) is given by the equation

\(\phi=5t^2+3t+16\)

The magnitude of induced emf in the coil at the fourth second will be

(1) 10 V

(2) 33 V

(3) 43 V

(4) 108 V

Given: Magnetic flux (ϕ) = 5t^{2 }+ 3t + 16

induced emf = \(-\frac{d\phi}{dt}\)

\(\epsilon\)=\(\frac{d(5t^2+3t+16}{dt}\) =10t+3

Therefore induced e.m.f. , when t=3,

\(|\epsilon_3|=(10\times3)+3=33 V\)

induced e.m.f. , when t=4 ,

\(|\epsilon_4|=(10\times4)+3=43 V\)

Therefor e.m.f. induced in the fourth second

=\(|\epsilon_4|-|\epsilon_3|=43-33=10V\)