Answer to Question #99148 in Electricity and Magnetism for Kim

Question #99148
Two coils, held in fixed positions, have a mutual inductance of 100 μH. What is the peak voltage in one when a sinusoidal current given by I (t) = (10.0 A) sin
(1 000t) is in the other coil?
1
Expert's answer
2019-11-22T10:55:56-0500


From the conditions of the problem we have

M=100106=1104[H]M=100\cdot 10^{-6}=1\cdot 10^{-4}[H]

ω=1000[rad]\omega=1000[rad]

Im=10[A]I_m=10[A]

I=0I=0

We write the second Kirchhoff law for the amplitude values of current and voltage in the second coil

IXL+Im(ωM)Um=0I\cdot X_L+I_m \cdot(\omega \cdot M)-U_m=0

or

0XL+Im(ωM)Um=00\cdot X_L+I_m \cdot(\omega \cdot M)-U_m=0

Im(ωM)Um=0I_m \cdot(\omega \cdot M)-U_m=0

where will we write

Um=Im(ωM)=1010001104=1[V]U_m=I_m \cdot(\omega \cdot M)=10\cdot 1000\cdot1\cdot10^{-4}=1[V]



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