Question

The magnetic flux in a closed circuit of resistance 20 Ω varies with time t as Φ = 4t^3 + 2t^2 – 15t + 3. Calculate the magnitude of induced emf at t = 1s.

(a) 3 V

(b) 4 V

(c) 5 V

(d) 6 V

The question was asked by my college director while I was bunking the class.

My question is from Faraday’s Law of Induction topic in division Electromagnetic Induction of Physics – Class 12

Answer 1

Right answer is (b) 4 V

Explanation: Given: Resistance = 20 Ω; Φ = 4t^3 + 2t^2 – 15t + 3

Required equation ➔ ε = \(\frac {-dΦ}{dt}\)

ε=\(\frac {-d(4t^3 + 2t^2 – 15t + 3)}{dt}\) = -(12t^2 + 4t – 15t + 3)

= -12 – 4 + 15 – 3   (Since t = 1s)

= 4 V

Therefore, the magnitude of induced emf is 4V.