Answer to Question #105860 in Electric Circuits for Zoya

Question

determine the value of load impedance (ZL) in order to get maximum power transfer at 100 Hz. What are the component values required to obtain this ZL?given that resistance is 200 ohm, inductance is 10mH.

Answer 1

A network that contains linear impedances and one or more voltage or current sources can be reduced to a Thevenin equivalent circuit.

A Thevenin equivalent circuit is shown in Figure1 with source internal impedance, $z=r+jx \ \Omega$ and complex load $Z=R+jX \ \Omega$

The maximum power transferred from the source to the load depends on the following four conditions.

1. When the load is purely resistive ($X=0$) and adjustable, maximum power transfer is achieved when

$$R=|z|=\sqrt{r^2+x^2}$$

2. When both the load and the source impedance are purely resistive ($X=x=0$), maximum power transfer is achieved when

$$R=r$$

3. When the load resistance $R$ and reactance $X$ are both independently adjustable, maximum power transfer is achieved when

$$X=-x \ \ \ \text{and}\ \ \ R=r$$

4. When the load resistance $R$ is adjustable with reactance $X$ fixed, maximum power transfer is achieved when

$$R=\sqrt{r^2+(x+X)^2}$$

Given that $r=200\ \Omega, f=100\ Hz, L=10\ mH.$

Then

$$R=r=200\ \Omega$$ $$X=-x=-j(2\pi f)L$$

$$X=-j2\pi(100\ Hz)(0.01\ H)=j(-2\pi)\ \Omega$$

$$Z=(200-2\pi j)\ \Omega$$