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Impedance Can Be Complex!

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

 

An AC generator of rms voltage E is connected in series with two reactive impedances,
$Z_1$ and $Z_2$, as shown below:

$\theta$ is the argument of $Z_1$ and $\phi$ is the argument of $Z_2$.

Find the power dissipated in $Z_2$

If the phase of $Z_2$ ($\phi$) is fixed whilst allowing the magnitude to vary, find the relationship between $Z_1$ and $Z_2$ when we achieve maximum power transfer to $Z_2$.