$1.80 \textrm{ mH}$

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This is College Physics Answers with Shaun Dychko. We are going to find the mutual inductance between these two coils by taking the absolute value of induced EMF because we don’t really care about directions here, so we will just take the EMF induced in the second coil equal the mutual inductance times the rate of change of current in the first coil and so we will multiply both sides by delta <i>T</i> over <i>I</i> and then we will solve for <i>M</i> and so the mutual inductance is the induced EMF times the time in which the current changes divided by the amount which current changes. So, its nine volts induced and then that happens in one milli-second and change in current is five amps. Because it gets switched off and so its goes from five amps it goes to zero is what implied by saying “switched off” and this makes 1.80 milli-henry is the mutual inductance.