The magnetic flux through a coil perpendicular to its plane is varying according to the relation ϕ = (5t³ + 4t² + 2t - 5) Weber. If the resistance of the coil is 5 ohm, then the induced current through the coil at t = 2 s will be,

CONCEPT:

• The induced EMF is written as;

           E = \(\frac{dϕ}{dt}\)

          here we have E as induced EMF and ϕ is flux through a coil.

• Also induced EMF is written as;

           E = IR

          Here E is as induced EMF, "I" is the current amd R is the resistance.

CALCULATION:

Given: ϕ = 5t3 + 4t2 + 2t - 5 Weber

Resistance, R = 5 Ω 

Time, t = 2 s

Now the induced EMF is written as;

 E = \(\frac{dϕ}{dt}\)

⇒ E = \(\frac{d(5t^3+4t^2+2t-5)}{dt}\)

⇒ E = 15t² + 8t+ 2

At t = 2 s

E = 15 (2)² + 8(2) +2

⇒ E = 60 +16 +2

⇒ E = 78 V

As we know that, E = IR

⇒ I = \(\frac{E}{R}\)

⇒ I = \(\frac{78}{5}\)

⇒ I = 15.6 A

Hence, option 1) is correct answer.