--- title: "Trickle charging and Ah/Wh efficiency (4 A, 12 h, 1.2 V)" subject: "Industrial Power Distribution and Illumination" chapter: 9 key: "semester_6/industrial_power_distribution_and_illumination:trickle-charging-4a-1-2v" source: https://www.bctengineer.com/q/semester_6/industrial_power_distribution_and_illumination/trickle-charging-4a-1-2v site: BCT Engineering --- # Trickle charging and Ah/Wh efficiency (4 A, 12 h, 1.2 V) Industrial Power Distribution and Illumination · Chapter 9: Emergency and Backup Supply Systems - Asked in: 2075 Bhadra, 8 marks; 2068 Bhadra (old course), 8 marks (asked 2 times) - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/industrial_power_distribution_and_illumination/trickle-charging-4a-1-2v - Whole chapter: https://www.bctengineer.com/md/semester_6/industrial_power_distribution_and_illumination/chapter-9 ## Question Explain trickle charging method for battery charging system. A lead acid cell is discharged at a steady current of 4 A for 12 hours, the average terminal voltage being 1.2 volt. To restore it to its original state of charge, a steady current at 3 A for 20 hours is required the average terminal voltage being 1.44 volt. Calculate the ampere-hour efficiency and watt-hour efficiency in this particular case. ## Short answer Trickle charging keeps an idle battery fully charged with a small current matching its self-discharge. For the lead-acid cell, ampere-hour efficiency is 80% (48 Ah out / 60 Ah in) and watt-hour efficiency is 66.67% (57.6 Wh out / 86.4 Wh in). ## Answer #### Trickle charging **Trickle charging** means connecting an idle, fully charged battery permanently to a charger that supplies a **very small current**, equal to its **self-discharge (local action) loss**, so that the battery remains fully charged and ready. - The trickle current is small, about 1% of the Ah capacity or less (for a healthy battery, as little as about 1 mA per Ah). - Normally the battery does not feed the load; it is called upon only when the mains fails. - Applications: emergency lights, fire alarm panels, DG set starting batteries, telephone exchanges, switchgear control batteries. - The charger is a small transformer–rectifier with a series resistance or regulator to set the current. - Too high a current causes gassing and water loss; too low a current lets the battery sulphate. The specific gravity should be checked periodically. ```text 230 V AC ─►[Step-down]─►[Rectifier]─►[R]─┐ + │ [Battery] − │ ─────────────────────────────────────────┘ ``` #### Numerical **Given:** discharge 4 A for 12 h, average voltage 1.2 V; charge 3 A for 20 h, average voltage 1.44 V. **Ampere-hour efficiency** ```text Ah output = 4 × 12 = 48 Ah Ah input = 3 × 20 = 60 Ah η_Ah = 48 / 60 × 100 = 80 % ``` **Watt-hour efficiency** ```text Wh output = 48 × 1.2 = 57.6 Wh Wh input = 60 × 1.44 = 86.4 Wh η_Wh = 57.6 / 86.4 × 100 = 66.67 % ``` (Check: η_Wh = η_Ah × 1.2/1.44 = 0.8 × 0.8333 = 0.6667.) Watt-hour efficiency is lower than Ah efficiency because the cell is charged at a higher voltage than it gives on discharge. **Answer: η_Ah = 80 %, η_Wh = 66.67 %.** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is the trickle charge current, roughly? A. About C/10 B. 1-2% of the Ah capacity C. Equal to capacity D. About 50% of capacity Answer: B. It only offsets self-discharge, so it is very small. (Key point: Trickle current) 2. What happens if the trickle current is too high or too low? A. Too high: gassing and water loss; too low: sulphation B. Too high: sulphation; too low: gassing C. Both cause a short circuit D. No effect Answer: A. Current must be set correctly to avoid gassing or sulphation. (Key point: Over/under trickling) 3. With 4 A for 12 h out and 3 A for 20 h in, what is the Ah efficiency? A. 60% B. 66.7% C. 80% D. 125% Answer: C. 48 Ah / 60 Ah = 80%. (Key point: Ah efficiency) 4. What is the Wh efficiency (1.2 V discharge, 1.44 V charge)? A. 80% B. 83.3% C. 57.6% D. 66.67% Answer: D. 57.6 Wh / 86.4 Wh = 0.667, i.e. 0.8 x 1.2/1.44. (Key point: Wh efficiency) ## Close variants set in other exams - [Trickle charging and Ah/Wh efficiency (2.2 V, 2.44 V)](https://www.bctengineer.com/question.md?key=semester_6%2Findustrial_power_distribution_and_illumination%3Atrickle-charging-2-2v) — Industrial Power Distribution and Illumination, chapter 9, asked 3× ## Related in Industrial Power Distribution and Illumination - [Trickle charging and Ah/Wh efficiency (30 A, 6 h)](https://www.bctengineer.com/question.md?key=semester_6%2Findustrial_power_distribution_and_illumination%3Atrickle-charging-30a-6h) — Industrial Power Distribution and Illumination, chapter 9, asked 2× - [Lead-acid cell characteristics and charging](https://www.bctengineer.com/question.md?key=semester_6%2Findustrial_power_distribution_and_illumination%3Alead-acid-characteristics-charging) — Industrial Power Distribution and Illumination, chapter 9 - [Charging lead acid battery from AC source](https://www.bctengineer.com/question.md?key=semester_6%2Findustrial_power_distribution_and_illumination%3Alead-acid-ac-charger) — Industrial Power Distribution and Illumination, chapter 9 - [Emergency supply and Ah vs Wh efficiency](https://www.bctengineer.com/question.md?key=semester_6%2Findustrial_power_distribution_and_illumination%3Aemergency-supply-ah-wh-efficiency) — Industrial Power Distribution and Illumination, chapter 9 ## Related in other subjects - [Battery charger bridge: average current, efficiency](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Abattery-bridge-30v-avg-efficiency) — Power Electronics, chapter 2