Overview
This lecture demonstrates how to apply mesh analysis to a circuit problem, with a focus on setting up mesh currents, writing equations, solving for unknowns, and calculating power delivered by circuit elements.
Mesh Analysis Setup
- Mesh analysis involves assigning loop currents (mesh currents) to independent loops in the circuit.
- The direction (clockwise/counterclockwise) and labeling of mesh currents do not affect the final answers, only the signs in equations.
- The goal of this example is to find the power delivered by an 80V power supply using mesh analysis.
Writing Mesh Equations
- Assign mesh currents: I₁, I₂, I₃ to the three loops.
- Apply Kirchhoff’s Voltage Law (KVL) around each loop, summing voltage drops and equating them to zero.
- For shared resistors between loops, the current is the difference or sum of mesh currents depending on direction.
- Example mesh equation for Loop 1:
80 = 31I₁ + 26I₂ – 5I₃
- Example mesh equation for Loop 2:
0 = 26I₁ + 124I₂ + 90I₃
- Example mesh equation for Loop 3:
0 = –5I₁ + 90I₂ + 125I₃
Solving the System
- Solve the three equations simultaneously to find each mesh current.
- Solution: I₁ = 5 A, I₂ = –2.5 A, I₃ = 2 A.
- Negative current indicates actual direction is opposite to the assumed direction.
Power Calculation
- Power delivered by the 80V supply: P = V × I = –80 × 5 = –400 W (delivering 400 W).
- Power in the 8Ω resistor: P = I²R = (–2.5)² × 8 = 50 W (absorbed).
- Negative power for supply means it delivers power; positive power for resistor means it absorbs power.
Key Terms & Definitions
- Mesh Analysis — A circuit analysis method using KVL for independent loops to find currents.
- Mesh Current — Hypothetical current circulating around a defined loop in the circuit.
- KVL (Kirchhoff’s Voltage Law) — The sum of voltages around any closed loop equals zero.
- Power Delivered/Absorbed — Negative value means delivered by supply; positive means absorbed by circuit element.
Action Items / Next Steps
- Review one more video on mesh analysis.
- Practice solving circuits using both mesh and nodal analysis for comparison.