📘 Thevenin’s Theorem – Complete Theory & Detailed Worked Examples
🔹 1. Introduction
Thevenin’s Theorem is one of the most powerful network simplification tools. It allows us to convert any complex linear two-terminal network into a simple equivalent circuit consisting of a single voltage source (Vth) in series with a resistance (Rth).
In GATE and IES exams, Thevenin is frequently tested in numerical and conceptual form.
🔹 2. Statement
Any linear bilateral network with independent sources can be replaced by an equivalent voltage source Vth in series with a resistance Rth as seen from the load terminals.
🔹 3. Step-by-Step Procedure
Step 2: Find open-circuit voltage → Vth.
Step 3: Deactivate independent sources.
Voltage source → Short circuit.
Current source → Open circuit.
Step 4: Find equivalent resistance seen from load terminals → Rth.
Step 5: Reconnect load and apply Ohm’s Law.
🔹 4. Worked Example 1 – Simple Voltage Divider
Given:
- Voltage Source = 24V
- R1 = 4Ω
- R2 = 8Ω
- Load RL = 6Ω
Step 1: Remove RL
Step 2: Find Vth
Vth = 24 × (8 / (4+8)) Vth = 24 × (8/12) Vth = 16V
Step 3: Find Rth
Rth = (4×8)/(4+8) Rth = 32/12 Rth = 2.67Ω
Step 4: Load Current
I = 16/(2.67+6) I = 1.85A
🔹 5. Worked Example 2 – Two Branch Circuit
Given:
- Voltage Source = 30V
- R1 = 10Ω
- R2 = 20Ω
- Load RL = 15Ω
Step 1: Remove RL
Step 2: Find Vth
Vth = 30 × (20/30) Vth = 20V
Step 3: Find Rth
Rth = (10×20)/(10+20) Rth = 6.67Ω
Step 4: Load Current
I = 20/(6.67+15) I = 0.92A
🔹 6. Maximum Power Transfer Using Thevenin
Condition for maximum power:
RL = Rth
Maximum power formula:
Pmax = Vth² / (4Rth)
🔹 7. Common Mistakes in Exams
- Forgetting to remove load before finding Vth
- Incorrect deactivation of sources
- Confusing series and parallel while calculating Rth
- Sign errors in voltage divider
🎯 Final Summary
Thevenin simplifies complex circuits. It is extremely powerful when load changes. Mastering Thevenin improves numerical solving speed in GATE.
Thevenin Mastery = Network Simplification Power
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