Question

The magnetic flux through a loop of resistance 0.1 Ω is varying according to the relation Φ = 6t² + 7t + 1, where Φ is in mihiweber and t is in second. What is the emf induced in the loop at t = 1 s and the magnitude of the current?

Answer 1

Data: R = 0.1 Ω, Φ_m = 6t² + 7t + 1 mWb, t = 1 s

(i) The induced emf, |e| = \(\cfrac{dΦ_m}{dt}\) = \(\cfrac d{dt}\)(6t² + 7t + 1)

= (12t + 7) mV 

= 12(1) + 7 = 19 mV

(ii) The magnitude of the current = \(\cfrac{[e]}R\)

= \(\cfrac{19mV}{0.1Ω}\) = 190 mA