Question

UI TU
The magnetic flux passing through a coil is
o = (20 cos 5πt + t^2 + 50t + 25) weber. What will
be the induced emf at t = 1 s?
(1) 52 V
(2) 72 V
(3) 1001 V
(4) (1001 + 50) V​

Answer 1

Answer: 52 V

Explanation:

Φ = 20 cos 5πt + t² +50t + 25

dΦ/dt = -20 sin 5πt × 5π +2t +50

= -20 sin 5π × 5π +2 +50

= 52 V

Answer 2

The correct answer is option (a) 52 V.

Given,

The magnetic flux passing through coil is Φ = (20 cos 5πt + t² +50t + 25) weber.

To Find,

The inducer emf at t = 1 s.

Solution,

The formula for calculating the induced emf is differentiating the given emf a with respect to time i.e dΦ/dt.

Now,

Φ = 20 cos 5πt + t² +50t + 25

So,

dΦ/dt = -20 sin 5πt × 5π +2t +50

Putting the value of t = 1s.

dΦ/dt = -20 sin 5π × 5π +2 +50

Induced emf at t= 1 s = dΦ/dt = 52 V

Hence, the induced emf at t = 1s is 52 V.

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