For 0 ≤ t ≤ 6 s, the magnetic flux through a coil is given by
Φ(t)=0.05t2−0.30t(Wb).
The coil has 100 turns and resistance 2 Ω.
a. (i) Derive an expression for the induced emf ε(t) as a function of time.
b. (ii) Determine the instants within the interval 0–6 s when the induced emf is zero.
c. (iii) Obtain an expression for the instantaneous power dissipated in the coil and hence calculate the total thermal energy produced in the coil between t = 0 s and t = 6 s.
d. (iv) Sketch on the same set of axes the graphs of Φ(t) and ε(t) for 0 ≤ t ≤ 6 s, indicating critical points obtained above.