Practice Problem 13.1 Magnetic Coupled

Determine the voltage $V_{o}$ in figure below

 Answer

$V_{1}=200\angle 45^\circ$

Loop 2 :

$(10+j5)I_{2}+jI_{1}=0$
$I_{1}=(-5+10j)I_{2}$

Loop 1 :

$(4+j8)I_{1}+jI_{2}=200\angle45^\circ$
$(4+j8)(-5+j10)I_{2}+jI_{2}=200\angle45^\circ$
$(-100+j)I_{2}=200\angle45^\circ$
$100\angle180^\circ I_{2}=200\angle45^\circ$
$I_{2}=\frac{200\angle45^\circ}{100\angle180^\circ }$
$I_{2} = 2\angle(-135)^\circ$

$V_{o} = 10I_{2} = 20\angle(-135)^\circ$

Note : Use this Calculator : https://www.intmath.com/complex-numbers/convert-polar-rectangular-interactive.php