The Class Notes

4 jan 2010

$Limit\ A\ \to \infty :$

$X_{0}\ ={\frac {1}{\beta }}X_{s}\ \Rightarrow V_{0}={\frac {R_{1}+R_{2}}{R_{1}}}V_{in}$

$X_{i}\ =0$

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

$V_{in}\ =V_{0}({\frac {R_{1}}{R_{1}+R_{2}}})$.

$V_{0}\ ={\frac {1}{({\frac {R_{1}}{R_{1}+R_{2}}})}}V_{in}$

Magnetic Circuits

jan 6 2010

${\vec {F}}\ =q{\vec {v}}\times {\vec {B}}$

$d{\vec {F}}\ =Id{\vec {l}}\times {\vec {B}}$

${\mathcal {F}}=Hl_{1}+Hl_{2}$

$V\ =R_{1}I+R_{2}I$

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

Magnetic Equations

$\int {\vec {H}}d{\vec {l}}={\mathcal {F}}$

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

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

$\int {\vec {B}}d{\vec {s}}=\phi \thickapprox BA_{rea}\ Magnetic\ Flux$

${\mathcal {R}}\equiv Reluctance\ {\frac {\mathcal {F}}{\phi }}={\frac {Ni}{\phi }}$

${\vec {B}}=\mu {\vec {H}}\ Assumes\ Linearity$

${\mathcal {R}}{\frac {l}{\mu A}}$

B H field histogram pic

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

Magnetic Circuits Examples

What about chancing currents, etc.?

Picture 5

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