--- title: "Maximum power in bridge load RL" subject: "Basic Electrical Engineering" chapter: 3 key: "semester_1/basic_electrical_engineering:max-power-bridge-rl-100v" source: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/max-power-bridge-rl-100v site: BCT Engineering --- # Maximum power in bridge load RL Basic Electrical Engineering · Chapter 3: Network Theorems - Asked in: 2071 Chaitra, 8 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/max-power-bridge-rl-100v - Whole chapter: https://www.bctengineer.com/md/semester_1/basic_electrical_engineering/chapter-3 ## Question Determine the value of load resistance RL to receive maximum power from the source. Also find the maximum power delivered to the load in the circuit shown in figure below: [Figure: 100 V source feeding a bridge; upper arms 10 Ω and 20 Ω, lower arms 30 Ω and 40 Ω; variable load RL connected across the bridge between the middle nodes.] ## Short answer Thevenin voltage across the bridge is 8.33 V and Thevenin resistance is 20.83 Ω. Maximum power transfer requires RL = 20.83 Ω, and the maximum power is 0.833 W. ## Answer #### Reading the figure The 100 V source (+ on top) feeds a bridge. Top vertex T and bottom vertex B are joined to the source. Upper arms: 10 Ω (T to left node X) and 20 Ω (T to right node Y). Lower arms: 30 Ω (X to B) and 40 Ω (Y to B). R_L is connected between X and Y. ```text T (+100 V) / \ 10 Ω 20 Ω / \ X --[R_L]-- Y \ / 30 Ω 40 Ω \ / B (0 V) ``` #### Step 1: Thevenin voltage across X-Y (R_L removed) V_X = 100 × 30/(10 + 30) = 75 V V_Y = 100 × 40/(20 + 40) = 66.67 V V_th = V_X − V_Y = **8.33 V** #### Step 2: Thevenin resistance (source shorted, T and B joined) From X: 10 Ω ∥ 30 Ω = 7.5 Ω From Y: 20 Ω ∥ 40 Ω = 13.33 Ω R_th = 7.5 + 13.33 = **20.83 Ω** #### Step 3: Maximum power R_L = R_th = **20.83 Ω** P_max = V_th²/(4 R_th) = 8.333²/(4 × 20.833) = 69.44/83.33 = **0.833 W** **Answer: R_L = 20.83 Ω; P_max = 0.833 W** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How is V_th found? A. V_X - V_Y = 75 - 66.67 = 8.33 V B. 100 V C. 75 V D. 0 V Answer: A. Each side divides the 100 V. (Key point: V_th) 2. How is R_th found? A. 10 + 20 + 30 + 40 B. Source shorted: (10||30) + (20||40) = 20.83 ohm C. (10+20)||(30+40) D. 10||20 Answer: B. T and B are joined, giving two parallel pairs in series. (Key point: R_th) 3. What R_L gives maximum power? A. 100 ohm B. 8.33 ohm C. 20.83 ohm D. 41.7 ohm Answer: C. R_L = R_th. (Key point: R_L) 4. What is P_max? A. 8.33 W B. 0.417 W C. 1.67 W D. 0.833 W Answer: D. 8.333^2/(4 x 20.83). (Key point: P_max) ## Related in Basic Electrical Engineering - [Find RL for maximum power (delta network)](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Amax-power-rl-10v-20-60-90) — Basic Electrical Engineering, chapter 3 - [Find RL for maximum power, 10 V network](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Amax-power-rl-10v-2-ohm-network) — Basic Electrical Engineering, chapter 3 - [Find RL for maximum power and Pmax](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Amax-power-rl-8v-4v-6-ohm) — Basic Electrical Engineering, chapter 3 - [Find R for maximum power, 10 A and 48 V](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Amax-power-r-10a-48v) — Basic Electrical Engineering, chapter 3 - [Find R for maximum power to load](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Amax-power-load-4-ohm-find-r) — Basic Electrical Engineering, chapter 3 - [Current in 20Ω using star-delta transformation](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Astar-delta-current-20-ohm-2v) — Basic Electrical Engineering, chapter 2 ## Related in other subjects - [Superposition theorem and maximum power to RL](https://www.bctengineer.com/question.md?key=semester_1%2Ffundamental_of_electrical_and_electronics_engineering%3Asuperposition-max-power-transfer) — Fundamental of Electrical and Electronics Engineering, chapter 1 - [Bridge rectifier feeding R and dc source](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Abridge-rectifier-dc-source-load) — Power Electronics, chapter 2 - [Unbalanced source feeding star load](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Aunbalanced-source-star-load-components) — Power System Analysis II, chapter 4 - [AVL tree for 10 20 30 50 45 40 8 5 3](https://www.bctengineer.com/question.md?key=semester_4%2Fdata_structure_and_algorithm%3Aavl-build-10-20-30) — Data Structure and Algorithm, chapter 6