gen-define-norton-s-theorem-and-give-one-short-worked-example-d4aa

Define Norton's theorem and give one short worked example.

# Norton's Theorem **Definition:** Norton's theorem states that any linear electrical network with voltage sources, current sources, and resistances can be replaced by an equivalent circuit consisting of a single **current source (IN)** in **parallel** with a single **resistance (RN)**. Where: - **IN** = Norton current (short-circuit current across the terminals) - **RN** = Norton resistance (resistance seen from the terminals with all independent sources deactivated) --- ## Worked Example Find the Norton equivalent circuit for the following network across terminals A-B: ``` 10Ω 20Ω A ○----[10Ω]----+----[20Ω]----○ B | 12V (-) | GND ``` **Solution:** **Step 1: Find IN (short-circuit current)** - Short terminals A-B - The 20Ω resistor is bypassed - Current from 12V source through 10Ω: I = 12V/10Ω = 1.2A - **IN = 1.2 A** (flowing from A to B) **Step 2: Find RN** - Deactivate the voltage source (replace with short circuit) - Looking from terminals A-B: RN = 10Ω ∥ 20Ω - **RN = (10 × 20)/(10 + 20) = 200/30 = 6.67Ω** **Norton Equivalent:** - Current source: **IN = 1.2 A** - Parallel resistance: **RN = 6.67Ω**