The current through a coil as a function of time is represented by the equation

Question

The current through a coil as a function of time is represented by the equation I(t) = Ae-bt sin(at), where A = 5.25 A, b = 1.75 x 10-2 s-1, and ? = 375 rad/s. At t = 0.790 s, this changing current induces an emf in a second coil that is close by. If the mutual inductance between the two coils is 4.14 mH, determine the induced emf. (Assume we are using a consistent sign convention for both coils. Include the sign of the value in your answer.) 3.56 What is the rate at which the current changes in this case? How does the induced emf depend on the rate of change of current? V

Explanation / Answer

Induced voltage is given by V= -M*di/dt = -0.00414*d(I(t))/dt

But, di/dt = d(Ae^-bt*sin(wt))/dt = -be^-bt*sin(wt) + we^-bt*cos(wt)

So, di/dt = e^-bt(w*cos(wt)-b*sin(wt))

Using given values

di/dt = 163.6

So, V= -0.00414*163.6 = -0.677V

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.