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## Homework Statement

A real voltage source can be expressed as an ideal voltage source that is in series with a resistor that represents the inner resistance of the voltage source. This voltage source is a EMF and it is also in series with another resistor. Suppose both the EMF resistor ##R_\varepsilon## and the second resistor ##R_2## have complex impedance. Determine a) The current, b) the non-dc power that is dissipated in the second resistor and c) The requirements to achieve maximum dissipated power in the second resistor.

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## Homework Equations

##\tilde{v}=\tilde{i}z##

##z_ts=z_1+z_2+\cdots##

##z=|z|e^{j\phi}##

## The Attempt at a Solution

For part a) the total impedance will be given by ##z_t=z_1+z_2=(R_\varepsilon +ja)+(R_2+jb)=(R_\varepsilon+R_2)+j(a+b)## so ##|z|=\sqrt{(R_\varepsilon+R_2)^2+(a+b)^2}## and ##\phi=tan^{-1}(\frac{a+b}{R_\varepsilon+R_2})## then from ##\tilde{i}=\frac{\tilde{v}}{z}##

$$\tilde{i}=\frac{ve^{-j\phi}}{\sqrt{(R_\varepsilon+R_2)^2+(a+b)^2}} \\

i=\frac{v\cos(\phi)}{\sqrt{(R_\varepsilon+R_2)^2+(a+b)^2}}

$$

now for b) would the non-dc power dissipated in the second resistor be ##P=i\Im{(R_2)}=ibj##?

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