The magnetic flux through each turn of a coil having 200 turns is given as (t² $-$ 1) x 10^-3 Wb, where t is in second. The emf induced in the coil at t = 3s is

0.7 V

1.2 V

0.8 V

0.9 V

Solution

0.8 V

Given magnetic flux

$ϕ = (t^{2} - 2 t) \times 10^{- 3}$

On differentiating with respect to time t

$\frac{dϕ}{dt} = (2 t - 2) \times 10^{- 3}$

At time t = 3s

${|\frac{dϕ}{dt}|}_{t = 3 s} = (2 \times 3 - 2) \times 10^{- 3}$

= 4 × 10^-3 Wb s^-1

Now

$|e| = N |\frac{dϕ}{dt}|$

= 200 × 4 × 10^-3

= 800 × 10^-3

⇒ $|e| = 0.8 V$

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