gen-define-thevenin-s-theorem-and-give-one-short-worked-example-e435

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

# Thevenin's Theorem **Definition:** Any linear electrical network with 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 single resistance (R_TH) from the perspective of any two terminals. Where: - **V_TH** (Thevenin voltage) = open circuit voltage across the terminals - **R_TH** (Thevenin resistance) = resistance seen from the terminals with all independent sources deactivated (voltage sources shorted, current sources opened) ## Worked Example Find the current through the 10Ω load resistor using Thevenin's theorem: ``` 5Ω 10Ω (load) ┌───┐ 20V │ ├────┬────┬───┐ └───┘ │ │ │ 15Ω 10Ω │ │ │ │ └────┴───┘ ``` **Step 1: Find V_TH (remove load, find open circuit voltage)** Current through circuit: I = 20V/(5Ω + 15Ω) = 1A V_TH = voltage across 15Ω = 1A × 15Ω = **15V** **Step 2: Find R_TH (deactivate source, find resistance)** Short the 20V source: R_TH = 15Ω || 5Ω = (15 × 5)/(15 + 5) = **3.75Ω** **Step 3: Apply Thevenin equivalent** Current through 10Ω load: I_load = V_TH/(R_TH + R_load) = 15V/(3.75Ω + 10Ω) = **1.09A**