The magnetic flux passing through a metal ring varies with time `t` according to `phi_(B)=6t^(3)-I8t^(2)` , `t` is in second. The resistance of the ring is `3Omega` . Determine the maximum current induced in the ring during the interval from `t=0` to `t=2sec` .

Explanation

`phi=6t^(3)-18t^(2)`
`e=-(dphi)/(dt)=-18t^(2)+36t`
`I=(e)/(R)=(-18t^(2)+36t)/(3)=-6t^(2)+12t`
I will be maximum when `(dI)/(dt)=-12t+12=0 implies t=1sec`
At `t=1sec`
`I=-6(1)^(2)+12(1)=6A`