The magnetic flux through a coil perpendicular to its plane is varying according to the relation  φ = ( 5 t^3 + 4t^2 + 2t – 5) weber …

Q: The magnetic flux through a coil perpendicular to its plane is varying according to the relation  φ = ( 5 t³ + 4t² + 2t – 5) weber . Calculate the induced current through the coil at t = 2 second. The resistance of the coil is 5 Ω .

Sol. φ = ( 5 t³ + 4 t² + 2t – 5)

|e| = dφ/dt = 15 t² + 8 t + 2

at t = 2 sec, e = 78 V

i × 5 = 15 × 4 + 8 × 2 + 2

⇒ i = 15.6 A .