If for a coil having L=2mH,current flowing through it is I=t'2e'-t,then time at which emf becomes zero is- a)2s b)1s c)3s d)4s answer fast.?

Question

Answer

Εmf.ε=Ldt​di​​=2×10−3dtd​(t2e−t)0=2×10−3(2te−t−e−tt2)t(2−t)e−t=02−t=0t=2sec

Answer

Answer

To find the time at which the emf becomes zero for a coil with an inductance of L=2mH and a current flowing through it given by I=t'2e'-t, we need to determine the time when the rate of change of current becomes zero.

Given:
Inductance L = 2mH = 0.002H
Current I = t'2e'-t

We know that the emf (ε) induced in a coil is given by Faraday's law of electromagnetic induction:
ε = -L(di/dt)

Here, ε is the emf induced, L is the inductance, and (di/dt) is the rate of change of current.

To find the time at which the emf becomes zero, we need to find the point where (di/dt) is zero.

Taking the derivative of the current equation with respect to time (t), we get:
di/dt = d/dt (t'2e'-t)
= 2t'e'-t - 2t'e'-t
= 2t'e'-t - 2t'e'-t
= 2t'e'-t - 2t'e'-t
= 0

Setting the derivative equal to zero, we have:
2t'e'-t - 2t'e'-t = 0

Simplifying the equation, we get:
2t'e'-t = 2t'e'-t

Since the exponential term (e'-t) is common on both sides, it cancels out, leaving us with:
2t' = 2t'

This equation is true for all values of t. Therefore, the rate of change of current (di/dt) is always zero for the given current equation.

Hence, the emf becomes zero at any time t.

Therefore, there is no specific time at which the emf becomes zero in this case.

Answer: There is no specific answer.

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