Question

A varying magnetic flux linking a coil is given by Φ = Xt2. If at time t=3s, the emf induced is 9V, then the value of X is

Answer 1

To find the value of X, we can use Faraday's law of electromagnetic induction, which states that the electromotive force (emf) induced in a coil is equal to the rate of change of magnetic flux through the coil. Mathematically, it is expressed as:

EMF = -dΦ/dt

In this case, Φ = Xt^2. To find dΦ/dt, we'll take the derivative with respect to time (t):

dΦ/dt = d/dt (Xt^2)

Using the power rule of differentiation, we get:

dΦ/dt = 2Xt

Now, you mentioned that at time t = 3s, the emf induced is 9V. So, we can plug in these values into the equation:

9V = 2X * 3s

Now, solve for X:

9V = 6X

Divide both sides by 6:

X = 9V / 6

X = 3/2

So, the value of X is 3/2 or 1.5.

Step-by-step explanation: