The Class Notes

4 jan 2010

$$\begin{gathered} Limit \\ A \\ \to \mathrm{\infty }: \end{gathered}$$

$$\begin{gathered} X_0 \\ =\frac{1}{\beta }{X}_s \\ \Rightarrow V_0=\frac{R_1+R_2}{R_1}{V}_{in} \end{gathered}$$

$$\begin{gathered} X_i \\ =0 \end{gathered}$$

Picture drawn by Kirk Betz based on drawing by Dr. Frohnes, lecture Jan. 4, 2010

$$\begin{gathered} V_{in} \\ =V_0(\frac{R_1}{R_1+R_2}) \end{gathered}$$.

$$\begin{gathered} V_0 \\ =\frac{1}{(\frac{R_1}{R_1+R_2})}{V}_{in} \end{gathered}$$

Magnetic Circuits

jan 6 2010

$$\begin{gathered} \overrightarrow{F} \\ =q\overrightarrow{v}\times \overrightarrow{B} \end{gathered}$$

$$\begin{gathered} d\overrightarrow{F} \\ =Id\overrightarrow{l}\times \overrightarrow{B} \end{gathered}$$

${ℱ}=H{l}_1+H{l}_2$

$$\begin{gathered} V \\ =R_{1}I+R_{2}I \end{gathered}$$

Picture drawn by Kirk Betz based on drawing by Dr. Frohnes, lecture Jan. 6, 2010

Magnetic Equations

$\int \overrightarrow{H}d\overrightarrow{l}={ℱ}$

$\oint \overrightarrow{H}d\overrightarrow{l}=Ni=\sum _{n}Hl+Ni=0$

$\oint \overrightarrow{B}d\overrightarrow{s}=0$

$$\begin{gathered} \int \overrightarrow{B}d\overrightarrow{s}=\varphi \approx B{A}_{rea} \\ Magnetic \\ Flux \end{gathered}$$

$$\begin{gathered} {ℛ}\equiv Reluctance \\ \frac{{ℱ}}{\varphi }=\frac{Ni}{\varphi } \end{gathered}$$

$$\begin{gathered} \overrightarrow{B}=\mu \overrightarrow{H} \\ Assumes \\ Linearity \end{gathered}$$

${ℛ}\frac{l}{\mu A}$

Picture drawn by Kirk Betz based on drawing by Dr. Frohnes, lecture Jan. 6, 2010

Pictures drawn by Kirk Betz based on drawing by Dr. Frohnes, lecture Jan. 6, 2010

Magnetic Circuits Examples

What about chancing currents, etc.?

Picture 5

$\oint \overrightarrow{H}d\overrightarrow{l}=Ni$