What is the peak emf in one coil when the current in the other coil is I(t) = 15.0 sin(1.25 *10^3 t), where I is in amperes and t is in seconds?

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Two coils, held in fixed positions, have a mutual inductance of 105 µH. What is the peak emf in one coil when the current in the other coil is I(t) = 15.0 sin(1.25 image 103t), where I is in amperes and t is in seconds?
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asked Mar 6, 2012 in Physics by awesome ~Expert~ (1,479 points)
    

1 Answer

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Best answer

The relation between emf and mutual inductance is as follows:

which basically means:

Emf of 2 = - Mutual inductance of 1 on 2  *  change in current of 1 divided by time

Since we are given I(t), we need to take the derivative with respsect to t to get dI/dt

I(t) = 15.0 sin(1.25 image 103t)

so

dI/dt = 15*1.25*10^3 * cos(1.25*10^3 t)

which has a max value when t = 0, so cos goes to 1

since we now know both dI/dt an d the mutual inductance, the Emf can be calculated form the first equation.

 

answered Mar 15, 2012 by Joey33 ~Expert~ (1,216 points)
selected Mar 15, 2012 by awesome

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