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## Homework Statement

[Broken]

a) For the circuit shown, determine the impedance Z

_{L}that results in maximum average power transfer to the Z

_{L}

b) What is the maximum average power transferred to the load impedance?

## Homework Equations

Thevenin, Norton procedures, voltage division, current division, etc etc

Max. average power = 1/2(Vs/Rs + RL)

^{2}* RL

P

_{L}= (V/(R

_{s}+ R

_{L}))

^{2}*R

_{L}

R

_{s}= R

_{L}

J

_{s}= -J

_{L}

## The Attempt at a Solution

I actually do not know how specifically for here how to get the equivalent impedance for the load, but I assume it's the same as finding Thevenin resistance so...

5Ω || 20Ω = 4Ω

4+3j || -6j =

=(1/4+3j + -1/6j)

^{-1}

=[ (6j-4-3j)/(24j-18) ]

^{-1}

= 24j-18 / 3j-4

multiplying by conjugate now:

=> * (-3j-4)/(-3j-4)

= (-72j

^{2}- 96j + 54j + 72)/(-9j

^{2}- 12j + 12j + 16)

= (72 + 72 -42j)/25

= 144-42j/25

=5.76 - 1.68j

R

_{Th}= 5.76Ω - 1.68jΩ

Z

_{L}= 5.76 + 1.68jΩ

Now

average power = 1/2*(20/(5.76 + 5.76))

^{2}*5.76 = 8.68W

Not sure if this is right

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