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📘 Norton’s Theorem – Definition & Full Worked Examples

                                      

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🔹 Definition of Norton’s Theorem

Norton’s Theorem states that any linear, bilateral two-terminal network can be replaced by an equivalent circuit consisting of a current source (I_N) in parallel with a resistance (R_N) as seen from the load terminals.

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🔹 Step-by-Step Solution Method

Step 1: Remove load resistor (RL).

Step 2: Find Short Circuit Current across load terminals.
This current = I_N (Norton Current).

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

Step 4: Find equivalent resistance from terminals.
This = R_N.

Step 5: Draw Norton equivalent:
Current source I_N in parallel with R_N.

Step 6: Reconnect RL and use Current Division Rule.

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🔹 Example 1 – Basic Norton Example

Given:

• Voltage Source = 12V
• Series Resistor = 6Ω
• Load RL = 3Ω

Step 1: Remove Load

Step 2: Find Short Circuit Current (IN)

If load terminals are shorted:

IN = V / R

IN = 12 / 6

IN = 2A

Step 3: Find RN

Deactivate voltage source → Short circuit.

RN = 6Ω

Step 4: Load Current

Using Current Division:

I_L = IN × (RN / (RN + RL))

I_L = 2 × (6 / (6 + 3))

I_L = 2 × (6/9)

I_L = 1.33A

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🔹 Example 2 – Voltage Divider Type Circuit

Given:

• Voltage Source = 24V
• R1 = 4Ω
• R2 = 8Ω
• Load RL connected across R2

Step 1: Remove Load

Step 2: Find Norton Current

First find Thevenin voltage:

Vth = 24 × (8 / (4+8)) = 16V

Rth = (4×8)/(4+8) = 2.67Ω

IN = Vth / Rth

IN = 16 / 2.67

IN = 6A

Step 3: RN = Rth = 2.67Ω

Step 4: Load Current

I_L = 6 × (2.67 / (2.67 + RL))

(Substitute RL value if given)

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🔹 Example 3 – Maximum Power Using Norton

Given:

• IN = 4A
• RN = 5Ω

Condition for Maximum Power

RL = RN

RL = 5Ω

Maximum Power

Pmax = (IN² × RN) / 4

Pmax = (4² × 5) / 4

Pmax = (16 × 5) / 4

Pmax = 20W

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🎯 Important Exam Insights

• Norton and Thevenin are dual theorems
• RN = Rth always
• IN = Vth / Rth
• Current division mistakes are common traps
• Frequently asked in GATE & IES

⚡ Master Norton – You Master Parallel Networks ⚡