Latest revision as of 17:10, 19 January 2010

2.10

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

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

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

$V_{o} + 2 - 5 = 0 ⟹ V_{o} = 3$

Nodal equation at $V_{+}$

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

Nodal equation at $V_{-}$

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

@@ 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=