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📘 Thevenin’s Theorem – Definition, Method & Quality Worked Examples

                                                

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🔹 Definition of Thevenin’s Theorem

Thevenin’s Theorem states that any linear, bilateral two-terminal network containing voltage sources, current sources, and resistances can be replaced by an equivalent circuit consisting of a single voltage source (V_th) in series with a resistance (R_th) as seen from the load terminals.

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🔹 When to Use Thevenin?

• When circuit is complex
• When load resistor changes frequently
• To simplify analysis
• To calculate maximum power transfer

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🔹 Step-by-Step Solution Method

Step 1: Remove the load resistor (RL).

Step 2: Find open-circuit voltage across load terminals.
This voltage = Vth (Thevenin Voltage).

Step 3: Deactivate all independent sources.
• Voltage source → Short circuit
• Current source → Open circuit

Step 4: Find equivalent resistance seen from load terminals.
This resistance = Rth (Thevenin Resistance).

Step 5: Reconnect load resistor.
Use Ohm’s Law:
I = Vth / (Rth + RL)

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🔹 Example 1 – Simple Voltage Divider

Given:

• Voltage Source = 20V
• R1 = 4Ω
• R2 = 6Ω
• Load RL = 5Ω (connected across R2)

Step 1: Remove Load

Step 2: Find Vth

Voltage Divider Rule:

Vth = 20 × (6 / (4 + 6))

Vth = 20 × (6/10)

Vth = 12V

Step 3: Find Rth

Deactivate source → Short circuit.

Rth = (4 × 6) / (4 + 6)

Rth = 24 / 10

Rth = 2.4Ω

Step 4: Load Current

Total Resistance = 2.4 + 5 = 7.4Ω

I = 12 / 7.4

I = 1.62A

Final Answer: Load Current = 1.62A

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🔹 Example 2 – Current Source Included

Given:

• Current Source = 5A
• Parallel resistor = 10Ω
• Load RL = 5Ω

Step 1: Convert to Thevenin

Open-circuit voltage:

Vth = I × R = 5 × 10

Vth = 50V

Step 2: Find Rth

Deactivate current source → Open circuit.

Rth = 10Ω

Step 3: Load Current

Total Resistance = 10 + 5 = 15Ω

I = 50 / 15

I = 3.33A

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🔹 Example 3 – Maximum Power Condition

Given:

• Vth = 24V
• Rth = 6Ω

Find RL for Maximum Power

Condition:

RL = Rth

Therefore,

RL = 6Ω

Maximum Power

Pmax = Vth² / (4Rth)

Pmax = 24² / (4 × 6)

Pmax = 576 / 24

Pmax = 24W

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🎯 Important Exam Insights

• Thevenin simplifies large circuits
• Voltage divider is commonly used for Vth
• Parallel combination often appears in Rth
• Very frequent topic in GATE & IES

⚡ Master Thevenin – You Master Network Simplification ⚡