In Figure P15-1, (L_{1}=10 mathrm{mH}, L_{2}=5 mathrm{mH}, M=7 mathrm{mH}), and (v) (mathrm{S}(t)=100 sin 1000 t mathrm{~V}). (a)

Question:

In Figure P15-1, $L_{1}=10 \mathrm{mH}, L_{2}=5 \mathrm{mH}, M=7 \mathrm{mH}$, and $v$ $\mathrm{S}(t)=100 \sin 1000 t \mathrm{~V}$.

(a) Write the $i-v$ relationships for the coupled inductors using the reference marks in the figure.

(b) Solve for $i_{1}(t)$ and $i_{2}(t)$ when the output terminals are short-circuited $\left(v_{2}(t)=0 \mathrm{~V}ight)$.

(c) What is the largest value $M$ can be?

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