Question

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

पर्याय

• 15.6 A

• 16.6 A

• 17.6 A

• 18.6 A

Answer 1

The magnetic flux through a coil perpendicular to its plane is varying according to the relation Φ = (5t³ + 4t² + 2t − 5) Weber. If the resistant of the coil is 5 ohm, then the induced current through the coil at t = 2 sec will be 15.6 A.

Explanation:

Given: Φ = (5t³ + 4t² + 2t − 5)

t = 2

Resistor (r) = 5 ohm

According to Faraday’s Law, the magnitude of induced EMF is the derivative of magnetic flux (Φ) with respect to time (t).

e = `(d phi)/dt`

= `d/dt (5t^3) + d/dt (4t^2) + d/dt (2t) - d/dt (5)`

= 15t² + 8t + 2

= 15(2)² + 8(2) + 2

= 15(4) + 16 + 2

= 60 + 16 + 2

= 78 V

Using Ohm’s law:

 I = `V/R`

= `e/R`

= `78/5`

= 15.6 A