In an inductor of self-inductance 2 ~mH , current changes with time (in sec) according to the relation, I=(3 t^2-3 t+8) A . The emf becomes zero at

Step-by-step solution

The induced electromotive force (emf) in an inductor is given by the formula = -L dI dt . Given L = 2 mH = 2 10⁻³ H and I = 3t^2 - 3t + 8 . Differentiating the current I with respect to time t : dI dt = d dt (3t^2 - 3t + 8) = 6t - 3 . The emf becomes zero when dI dt = 0 . Setting the derivative to zero: 6t - 3 = 0 6t = 3 t = 3 6 = 0.5 sec . Answer: 0.5 sec