lecture_EE1C1_lec3_circuit_analysis_2025-09-15

📌 Overview

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🎯Learning Objectives

• Methods Visual Inspection ✅ 2025-09-28
• Nodal analysis ✅ 2025-09-28
• Mesh analysis ✅ 2025-09-28

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💡Key Concepts & Definitions

➗ Formulas

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✍️ Notes

1. Visual Inspection
   1. Definition
      1. Look at system and solve (equivalent resistances)
      2. Equations
   2. Pro:
      1. easy
   3. Cons:
      1. not systematic
      2. doen’t work with complicated system
2. Nodal analysis
   1. Definition: (algorithm)
      1. Bookkeeping
         1. Determine Nodes (amount of parts of a circuit not touching by wires)
         2. Choose ground node (node with lowest relative voltage)
         3. Current directions
      2. Equations
         1. Kirchhoff current equation: $\sum i=0$
         2. Fill Ohms Law: $V=IR$
      3. math: Solve equation
         1. solve for all unknows using formulas from step 2
   2. Pro:
      1. always works
   3. cons:
      1. lots of work
3. Mesh Analasys
   1. definition:
      1. only works for planar circuits (without overlapping wires)
      2. Find all “loops” and write them in same direction
      3. Define the equations for the current of every mesh/loop
      4. Write with KVL: $V=\sum iR$
         1. $\{\begin{array}{l}{v}_1=i_a{R}_1+(i_a-i_b)R_3\\ i_b{R}_2+v_2+(i_b-i_a)R_3=0\end{array}\Rightarrow \left[\begin{array}{cc}{R}_1+R_3& -R_3\\ -R_3& R_2+R_3\end{array}\right]\times \left[\begin{array}{c}{i}_a\\ i_b\end{array}\right]=\left[\begin{array}{c}{v}_1\\ -v_2\end{array}\right]$
         2. .
   2. pros:
      1. faster sometimes
   3. cons:
      1. doesnt work with

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🔗 Resources

• Presentation:

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❓ Post lecture

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📖 Homework