Overview
The lecture introduces mesh analysis, a circuit analysis technique that uses Kirchhoff’s Voltage Law (KVL) and Ohm’s Law to solve for unknown currents, demonstrated with a worked example.
Mesh Analysis Basics
- Mesh analysis (also called loop analysis) uses KVL to analyze electrical circuits by examining loops.
- Primarily used to find currents in a circuit, though it can also find voltages.
- Loops (meshes) are typically drawn clockwise, but can be reversed depending on sources and current directions.
Setting Up Mesh Equations
- Assign a current variable (I1, I2, I3, etc.) to each mesh.
- Use KVL: sum of voltage drops around a closed loop equals zero.
- Express resistor voltages using Ohm’s Law (V = IR), where current through shared resistors is determined by the difference or sum of mesh currents.
- For shared resistors, the current through the resistor is the algebraic sum (or difference) of adjacent loop currents, based on their directions.
Example Problem Steps
- Identify meshes and assign loop currents.
- Write KVL equations for each loop, expressing all voltages in terms of the assigned loop currents and resistances.
- For shared resistors, use (I_mesh1 - I_mesh2) × R or (I_mesh2 - I_mesh1) × R depending on current directions.
- Simplify equations to form a system of linear equations.
- Solve the system (e.g., using a calculator) to find each mesh current.
Calculating Desired Quantities
- To find the voltage across a specific resistor, determine the net current through it using relevant mesh currents (e.g., V = (I1 - I2) × R for the 8Ω resistor).
- In the example, calculated mesh currents: I1 = 5.6 A, I2 = 2 A, I3 = -0.8 A.
- Output voltage across the 8Ω resistor: (5.6 A - 2 A) × 8Ω = 28.8 V.
Key Terms & Definitions
- Mesh — A loop in a circuit that does not enclose other loops.
- Mesh Current — Hypothetical current circulating around a mesh.
- Kirchhoff’s Voltage Law (KVL) — The total sum of voltages around any closed circuit loop is zero.
- Ohm’s Law — The voltage across a resistor is the product of current through it and its resistance (V = IR).
Action Items / Next Steps
- Practice mesh analysis by setting up and solving KVL equations for multi-mesh circuits.
- Prepare for the next lecture by reviewing the example provided and attempting similar problems.