Find the induced current through a coil at t = 2 s if the magnetic flux through a coil is `phi= 6t^(3) + 12t^(2) + 5` and the resistance of the coil is `5 Omega`.

Explanation

To find the induced current through a coil at \( t = 2 \, \text{s} \), given the magnetic flux \( \phi = 6t^3 + 12t^2 + 5 \) and the resistance \( R = 5 \, \Omega \), we will follow these steps:

### Step 1: Calculate the Induced EMF
The induced EMF (\( \mathcal{E} \)) can be calculated using Faraday's law of electromagnetic induction, which states that:
\[ \mathcal{E} = -\frac{d\phi}{dt} \]
First, we need to differentiate the magnetic flux \( \phi \) with respect to time \( t \).
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