Thévenin Equivalent Circuit
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Overview
This MicroSim walks through the five-step process of finding and verifying a Thévenin equivalent circuit.
| Circuit Parameter | Value |
|---|---|
| Source voltage \(V_s\) | 12 V |
| Series resistance \(R_1\) | 4 Ω |
| Shunt resistance \(R_2\) | 8 Ω |
| Thévenin voltage \(V_{th}\) | 8 V |
| Thévenin resistance \(R_{th}\) | 2.67 Ω |
Stage-by-Stage Guide
| Stage | Action | What to observe |
|---|---|---|
| 1 | Load the sim | Original voltage-divider circuit with terminals A-B |
| 2 | Click Find Vth → | Open-circuit voltage across R₂ highlighted; \(V_{th} = 8\text{ V}\) |
| 3 | Click Find Rth → | Vs shorted; \(R_{th} = R_1 \| R_2 = 2.67\text{ Ω}\) |
| 4 | Click Show Equiv → | Thévenin circuit appears alongside the original |
| 5 | Click Connect Load → | Load RL attached to both; drag the slider to verify identical \(V_L\) and \(I_L\) |
Key Equations
Open-circuit voltage (Thévenin voltage):
\[V_{th} = V_s \times \frac{R_2}{R_1 + R_2} = 12 \times \frac{8}{4+8} = 8 \text{ V}\]
Thévenin resistance (with voltage source short-circuited):
\[R_{th} = R_1 \| R_2 = \frac{R_1 R_2}{R_1 + R_2} = \frac{4 \times 8}{4 + 8} = 2.67 \text{ Ω}\]
Load current and voltage (same for both circuits):
\[V_L = V_{th} \times \frac{R_L}{R_{th} + R_L}, \qquad I_L = \frac{V_{th}}{R_{th} + R_L}\]
Learning Objective
Students will explain how any linear circuit seen from two terminals can be represented by a single voltage source \(V_{th}\) in series with a single resistance \(R_{th}\) that produces identical terminal behavior for any load.
Lesson Plan
Prerequisites
- Ohm's Law and series/parallel resistor combinations
- Voltage divider rule
- Concept of a two-terminal (port) circuit
Suggested Classroom Use
- Before the sim — Ask students: "If you could only see the two output terminals of a black box, what measurements could you take to characterise it?"
- Stages 1-3 — Let students predict \(V_{th}\) and \(R_{th}\) before clicking each button. Check their calculations.
- Stage 4 — Discuss: "Why are these two circuits equivalent at the terminals even though they look different inside?"
- Stage 5 — Have students predict \(V_L\) and \(I_L\) for a specific RL, then verify with the slider.
Assessment
- Calculate \(V_{th}\) and \(R_{th}\) for a different source/resistor combination.
- Explain in words why \(R_{th}\) is found by short-circuiting independent voltage sources.
- Predict the I-V characteristic slope from \(R_{th}\) alone.
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