--- title: "Trickle charging and Ah/Wh efficiency (2.2 V, 2.44 V)" subject: "Industrial Power Distribution and Illumination" chapter: 9 key: "semester_6/industrial_power_distribution_and_illumination:trickle-charging-2-2v" source: https://www.bctengineer.com/q/semester_6/industrial_power_distribution_and_illumination/trickle-charging-2-2v site: BCT Engineering --- # Trickle charging and Ah/Wh efficiency (2.2 V, 2.44 V) Industrial Power Distribution and Illumination · Chapter 9: Emergency and Backup Supply Systems - Asked in: 2073 Magh, 2+3+3 marks - 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-2-2v - Whole chapter: https://www.bctengineer.com/md/semester_6/industrial_power_distribution_and_illumination/chapter-9 ## Question Explain trickle charging method for a battery charging system. A lead acid cell is discharged at a steady current of 4A for 12 hours, the average terminal voltage being 2.2V. To restore it to its original state of charge, steady current at 3A for 20 hours is required, the average terminal voltage being 2.44V. Calculate the ampere-hour efficiency and watt-hour efficiency in this particular case. ## Short answer Trickle charging supplies a small continuous current, about 1% of capacity, to offset self-discharge and keep a standby battery full. For the data, Ah output is 48 and input is 60, so Ah efficiency is 80%; Wh output is 105.6 and input is 146.4, so Wh efficiency is 72.13%. ## Answer #### Trickle charging **Trickle charging** keeps an idle battery fully charged by supplying a **very small continuous current equal to its self-discharge loss**. - The current is about 1% of the Ah capacity or less (for a healthy battery, as little as about 1 mA per Ah). - The charger (step-down transformer + rectifier + series resistance/regulator) remains permanently connected. - The battery feeds the load only when the mains fails; after that it is recharged normally and trickle charging resumes. - Used for emergency lighting, fire alarm, DG starting and switchgear batteries. ```text AC ─►[Transformer]─►[Rectifier]─►[R]─► + Battery − ``` #### Numerical **Given:** discharge 4 A × 12 h at 2.2 V average; charge 3 A × 20 h at 2.44 V average. **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 × 2.2 = 105.6 Wh Wh input = 60 × 2.44 = 146.4 Wh η_Wh = 105.6 / 146.4 × 100 = 72.13 % ``` **Answer: Ampere-hour efficiency = 80 %, watt-hour efficiency = 72.13 %.** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What current does trickle charging supply to a battery? A. A high current for a short time to recover a deeply discharged battery B. A very small continuous current equal to the battery's self-discharge loss C. A constant current of C/10 until fully charged D. A current that rises as the battery voltage falls Answer: B. Trickle charging only makes up the self-discharge of an idle battery, so it keeps it fully charged without overcharging. (Key point: Trickle charging principle) 2. Where is trickle charging typically used? A. Quick recovery of a battery in a workshop B. Equalising the cells of a large bank C. Keeping standby batteries such as emergency lighting and DG starting batteries full D. First charge of a new battery Answer: C. Idle standby batteries need only a tiny continuous current to stay full. (Key point: Use of trickle charging) 3. Discharge is 4 A for 12 h and charge is 3 A for 20 h. What is the ampere-hour efficiency? A. 60 % B. 72.13 % C. 125 % D. 80 % Answer: D. Ah out = 4 x 12 = 48 Ah, Ah in = 3 x 20 = 60 Ah, so efficiency = 48/60 = 80 %. (Key point: Ah efficiency) 4. With average voltages of 2.2 V on discharge and 2.44 V on charge, what is the watt-hour efficiency? A. 72.13 % B. 80 % C. 90 % D. 69.5 % Answer: A. Wh out = 48 x 2.2 = 105.6 and Wh in = 60 x 2.44 = 146.4, so 105.6/146.4 = 72.13 %. It is lower than the Ah efficiency because charging voltage exceeds discharge voltage. (Key point: Wh efficiency) ## Close variants set in other exams - [Trickle charging and Ah/Wh efficiency (4 A, 12 h, 1.2 V)](https://www.bctengineer.com/question.md?key=semester_6%2Findustrial_power_distribution_and_illumination%3Atrickle-charging-4a-1-2v) — 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