Skip to content

Commit

Permalink
Added 1.3
Browse files Browse the repository at this point in the history
  • Loading branch information
arturombug committed Aug 10, 2020
1 parent 3d9d8c9 commit 5178c1c
Show file tree
Hide file tree
Showing 2 changed files with 2 additions and 2 deletions.
Binary file modified Chapter1.pdf
Binary file not shown.
4 changes: 2 additions & 2 deletions Chapter1.tex
Original file line number Diff line number Diff line change
Expand Up @@ -25,7 +25,7 @@
to[R=$R_2$,v=$V_{2}$] (2,0)
to (0,0)
\end{circuit}
By LVK and Ohm's law \[ V = V_{1} + V_{2} = R_{1}\cdot I + R_{2} \cdot I = (R_{1}+R_{2}) \cdot I = R \cdot I \]
By KVL and Ohm's law \[ V = V_{1} + V_{2} = R_{1}\cdot I + R_{2} \cdot I = (R_{1}+R_{2}) \cdot I = R \cdot I \]
where \[\mans{R = R_{1} + R_{2}}\] is the resistance of $R_{1}$ and $R_{2}$ in series. Now, consider a simple parallel resistor circuit.

\begin{circuit}{fig:1.3.2}{A basic parallel circuit.}
Expand All @@ -36,7 +36,7 @@
to[R=$R_2$,i>^=$I_{2}$] (4,0)
to (0,0)
\end{circuit}
By LCK and Ohm's law \[ I = I_{1} + I_{2} = \frac{V}{R_{1}} + \frac{V}{R_{2}} = \left(\frac{1}{R_{1}}+\frac{1}{R_{2}}\right)\cdot V \]
By KCL and Ohm's law \[ I = I_{1} + I_{2} = \frac{V}{R_{1}} + \frac{V}{R_{2}} = \left(\frac{1}{R_{1}}+\frac{1}{R_{2}}\right)\cdot V \]
solving for V as a function of I we get
\[V = \dfrac{1}{\frac{1}{R_{1}}+\frac{1}{R_{2}}}\cdot I = \frac{R_{1}R_{2}}{R_{1}+R_{2}}\cdot I = R\cdot I \]
where \[\mans{R = \dfrac{1}{\frac{1}{R_{1}}+\frac{1}{R_{2}}} = \frac{R_{1}R_{2}}{R_{1}+R_{2}}}\] is the resistance of $R_{1}$ and $R_{2}$ in parallel.
Expand Down

0 comments on commit 5178c1c

Please sign in to comment.