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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.
Solution
Magnetic flux (ΦB) = (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
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