The magnetic flux linked with a coil is given by the equation: = 8t^2 + t + 10 . The e.m.f. induced in the coil at t = 3 seconds will be:

Step-by-step solution

The magnetic flux linked with the coil is given by = 8t^2 + t + 10 . The induced electromotive force (e.m.f.) in the coil is given by Faraday's law of induction: = - d dt . Differentiating the flux with respect to time t : d dt = d dt (8t^2 + t + 10) = 16t + 1 . The magnitude of the induced e.m.f. is | | = |-(16t + 1)| = 16t + 1 . The e.m.f. induced in the 3^ rd second refers to the instantaneous e.m.f. at t = 3 s. Substituting t = 3 into the expression for the magnitude of the e.m.f.: | | = 16(3) + 1 = 48 + 1 = 49