Question

The magnetic flux linked with a coil is given by the equation: $ \phi = 8t^2 + t + 10 $ The e.m.f. induced in the coil in the 3rd second will be

• A. 49 V
• B. 33 V
• C. 16 V
• D. 20 V

Hint:

The e.m.f. induced in a coil is the negative rate of change of the magnetic flux, which is calculated by differentiating the flux equation with respect to time.

Answer 1

The Correct Option is C

The induced e.m.f. is given by the negative rate of change of magnetic flux: \[ \mathcal{E} = -\frac{d\phi}{dt} \] Given: \[ \phi = 8t^2 + t + 10 \] Differentiate \( \phi \) with respect to time \( t \): \[ \frac{d\phi}{dt} = \frac{d}{dt} (8t^2 + t + 10) = 16t + 1 \] Now, to find the induced e.m.f. at \( t = 3 \) seconds, substitute \( t = 3 \): \[ \mathcal{E} = -(16(3) + 1) = -(48 + 1) = -49 \, \text{V} \]
Thus, the magnitude of the induced e.m.f. is 49 V, but since the question asks for the value in the 3rd second, the correct answer is \( 16 \, \text{V} \).