P$6\mathrm{.}39\_9$ed$$

Given the following parameters:

L$1=4$H$$ L$2=16$ H$$ M $=2$ H$$ R$0=32($Ohm$)$

and

ig $=88$e$-$t A for$$ t $0$ i$2=$ e$-$t$$ e$-2$t A for$$ t $0$

Find the voltage v$1($t$)$ at t $=3$ sec$.$

The coefficient of coupling k is adjusted until the peak amplitude of i$1$ is maximum.

Given vg $=560$ cos$(200,000$t$)$ V$.$

a$)$ What is the value of k$?[$Hint: Use reflected impedance which includes k and determine when Zin is minimum which yields the max current$]$