Answer to Question #99148 in Electricity and Magnetism for Kim

Question

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?

Answer 1

From the conditions of the problem we have

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

$\omega=1000[rad]$

$I_m=10[A]$

$I=0$

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

$I\cdot X_L+I_m \cdot(\omega \cdot M)-U_m=0$

or

$0\cdot X_L+I_m \cdot(\omega \cdot M)-U_m=0$

$I_m \cdot(\omega \cdot M)-U_m=0$

where will we write

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