Latest revision as of 16:10, 19 January 2010

2.10

${\frac {V_{o}-0}{1000}}+.002=0\Longrightarrow V_{o}=-2$

${\frac {V_{o}-5}{3000}}+.002=0\Longrightarrow V_{o}=-1$

${\frac {V_{o}-0}{15000}}=0\Longrightarrow V_{o}=0$

$V_{o}+2-5=0\Longrightarrow V_{o}=3$

Nodal equation at $V_{+}$

${\frac {V_{A}-V_{+}}{R_{A}}}+{\frac {V_{B}-V_{+}}{R_{B}}}=0\Longrightarrow V_{+}={\frac {V_{A}R_{B}+V_{B}R_{A}}{R_{B}+R_{A}}}$

Nodal equation at $V_{-}$

${\frac {V_{o}-V_{-}}{R_{2}}}+{\frac {0-V_{-}}{R_{1}}}=0\Longrightarrow V_{o}={\frac {(V_{A}R_{B}+V_{B}R_{A})(R_{1}+R_{2})}{(R_{B}+R_{A})R_{1}}}$

@@ Line 1: / Line 1: @@
 =2.10=
-==2.10a==
+===2.10a===
-<math>\frac{V_o-0}{1000}+.002=0,V_o=-2</math>
+<math>\frac{V_o-0}{1000}+.002=0 \Longrightarrow V_o=-2</math>
-==2.10b==
+===2.10b===
-<math>\frac{V_o-5}{3000}+.002=0, V_o=-1</math>
+<math>\frac{V_o-5}{3000}+.002=0 \Longrightarrow V_o=-1</math>
-==2.10c==
+===2.10c===
-<math>\frac{V_o-0}{15000}=0, V_o=0</math>
+<math>\frac{V_o-0}{15000}=0 \Longrightarrow V_o=0</math>
-==2.10d==
+===2.10d===
-<math>V_o+2-5=0, V_o=3\,</math>
+<math>V_o+2-5=0 \Longrightarrow V_o=3</math>
 =2.22=
+Nodal equation at <math>V_+</math>
+*<math>\frac{V_A-V_+}{R_A}+\frac{V_B-V_+}{R_B}=0 \Longrightarrow V_+=\frac{V_AR_B+V_BR_A}{R_B+R_A}</math>
+Nodal equation at <math>V_-</math>
+*<math>\frac{V_o-V_-}{R_2}+\frac{0-V_-}{R_1}=0 \Longrightarrow V_o=\frac{(V_AR_B+V_BR_A)(R_1+R_2)}{(R_B+R_A)R_1}</math>
 =2.43=
 =2.47=