Question

The flux linked with a coil at any instant is given by \( \Phi = 5t^2 - 25t - 150 \) (in SI units). The emf induced in the coil at \( t = 2 \) s is

• A. +5 V
• B. +3 V
• C. -1 V
• D. -5 V
• E. -3 V

Hint:

The induced emf can be calculated by differentiating the flux \( \Phi \) with respect to time and applying Faraday's Law of Induction.

Answer 1

The Correct Option is A

The emf induced in the coil is given by Faraday's Law of Induction: \[ \text{emf} = - \frac{d\Phi}{dt} \] Where: - \( \Phi = 5t^2 - 25t - 150 \) is the magnetic flux as a function of time. To find the emf at \( t = 2 \) s, we first differentiate \( \Phi \) with respect to time \( t \): \[ \frac{d\Phi}{dt} = \frac{d}{dt} (5t^2 - 25t - 150) \] \[ \frac{d\Phi}{dt} = 10t - 25 \] Now, substitute \( t = 2 \) s into the equation: \[ \frac{d\Phi}{dt} = 10(2) - 25 = 20 - 25 = -5 \] The emf is: \[ \text{emf} = - (-5) = +5 \, \text{V} \] Thus, the emf induced in the coil at \( t = 2 \) s is +5 V. Hence, the correct answer is (A) +5 V.