diff --git a/Chapter1.pdf b/Chapter1.pdf index 91303aa..e8a5029 100755 Binary files a/Chapter1.pdf and b/Chapter1.pdf differ diff --git a/Chapter1.tex b/Chapter1.tex index 82cbfc9..bd8a69b 100644 --- a/Chapter1.tex +++ b/Chapter1.tex @@ -118,7 +118,52 @@ \[I = \frac{0.5 \V}{5\k\Ohm + 20\k\Ohm} = \mans{0.02 \m\A} \quad \text{ and } \quad V = 0.02 \m\A \cdot 20\k\Ohm = \mans{0.4 \V}\] \end{enumerate} - + \ex{1.8} + \begin{enumerate} + \item In the first part, we have the following circuit: + \begin{circuit}{fig:1.8.1}{50\u A ammeter with 5k\Ohm\ internal + resistance (shown in blue) in parallel with shunt resistor.} + + (0,0) to[isource, l=$I$, -*] (0,2) + (0,2) to[short] (0,3); + \draw[blue] + (0,2) to[R=5k\Ohm, i>^=$I_m$, color=blue] (4,2) + (4,2) to node[draw, circle, fill=white] {A} (6,2); + \draw + (0,3) to[R=$R_s$, i>^=$I_s$] (6,3) + (6,3) to[short, -*] (6,2) + (6,2) to[short] (6,0) + (6,0) to[short] (0,0) + \end{circuit} + + We want to measure $I$ for 0-1 A, and the ideal ammeter measures + up to 50 $\mu\A$. To find what shunt resistance $R_s$ allows us to do so, + we set $I = 1 \A$ and $I_m = 50 \mu\A$. By KCL we know $I_s = 0.999950 \A$. + To determine $R_s$, we still need to find the voltage across it. We can + find this voltage by doing + \[V = I_m R_m = 50 \mu\A \cdot 5 \k\Ohm = 0.25 \V\] + Then we simply do + \[R_s = \frac{V}{I_s} = \frac{0.25 \V}{0.999950 \A} = \mans{0.25 \Ohm}\] + + \item In the second part, we have the following circuit: + \begin{circuit}{fig:1.8.2}{50\u A ammeter with 5k\Ohm\ internal + resistance (shown in blue) with a series resistor.} + + (0,0) to[V=$V$, invert, i^>=$I$] (0,2); + \draw[blue] + (0,2) to[R=5k\Ohm, color=blue] (2,2) + (2,2) to node[draw, circle, fill=white] {A} (4,2); + \draw + (4,2) to[R=$R_s$] (4,0) + (4,0) to[short] (0,0) + \end{circuit} + + We want to measure $V$ for 0-10 V, and the ideal ammeter measures up to + 50 $\mu\A$. To find the series resistance $R_s$, we set $V = 10\V$ and + $I = 50\mu\A$. Then we solve + \[\frac{V}{I} = 5\k\Ohm + R_s\] + \[R_s = \frac{10\V}{50\mu\A} - 5\k\Ohm = \mans{195\k\Ohm}\] + \end{enumerate} \ex{1.10} \begin{enumerate}