From the conditions of the problem we have
M=100⋅10−6=1⋅10−4[H]
ω=1000[rad]
Im=10[A]
I=0
We write the second Kirchhoff law for the amplitude values of current and voltage in the second coil
I⋅XL+Im⋅(ω⋅M)−Um=0
or
0⋅XL+Im⋅(ω⋅M)−Um=0
Im⋅(ω⋅M)−Um=0
where will we write
Um=Im⋅(ω⋅M)=10⋅1000⋅1⋅10−4=1[V]
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