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The magnetic flux passing through a coil...

The magnetic flux passing through a coil perpendicular to is plane is a function of time and is given by `Phi_(B)=(2t^(3)+4t^(2)+8t+8)` Wb. If he resistance of the coil is `5Omega,` determine the induced current through the coil at a time t = 3 second.

Text Solution

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Given : The magnetic flus
`Phi=(2t^(3)+4t^(2)+8t+8)Wb.`
Resistanced of the coil R `=5Omega`
To find :
Induced at through the coil I = ?
For time t = 3 s
Formula :
Induced emf `e=(dPhi_(B))/(dt)`
Solution :
`e=(d)/(dt)(2t^(3)+4t^(2)+8t+8)`
`e=6t^(2)+8t+8`
When t = 3s
`e=6xx(3)^(2)+8xx3+8`
= 54 + 24 + 8
e = 86 V
Induced current through the coil `I=(e)/(R)`
`I=(86)/(5)`
I = 17.2 A
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