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 10^{3}*t*), where *I* is in amperes and *t* is in seconds?

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+4 votes

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 10^{3}*t*)

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.

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