Question

The magnetic flux passing through a coil perpendicular to its plane is a function of time and is given by OB = (2t³ + 4t² + 8t + 8) Wb. If the resistance of the coil is 5 Ω, determine the induced current through the coil at a time t = 3 second.

Answer 1

Magnetic flux (Φ_B) = (2t³ + 8t² + 8t + 8)Wb

Resistance of the coil (R) = 5 Ω

time (t) = 3 second

Induced current through the coil, I = `"e"/"R"`

Induced emf, e = `("d"Φ_"B")/"dt" = "d"/"dt"`  ((2t³ + 4t² + 8t + 8) = 6t² + 8t + 8

Here time (t) = 3 second

e = 6(3)² + 8 × 3 + 8 = 54 + 24 + 8 = 86 V

∴ Induced current through the coil, I = `"e"/"R" = 86/5 = 17.2`A