---
title: "Trickle charging and Ah/Wh efficiency (30 A, 6 h)"
subject: "Industrial Power Distribution and Illumination"
chapter: 9
key: "semester_6/industrial_power_distribution_and_illumination:trickle-charging-30a-6h"
source: https://www.bctengineer.com/q/semester_6/industrial_power_distribution_and_illumination/trickle-charging-30a-6h
site: BCT Engineering
---

# Trickle charging and Ah/Wh efficiency (30 A, 6 h)

Industrial Power Distribution and Illumination · Chapter 9: Emergency and Backup Supply Systems

- Asked in: 2076 Bhadra, 4 marks; 2071 Bhadra, 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-30a-6h
- Whole chapter: https://www.bctengineer.com/md/semester_6/industrial_power_distribution_and_illumination/chapter-9

## Question

Explain the trickle charging method for a battery charging system. Calculate the (i) ampere-hour efficiency and (ii) watt-hour efficiency of a secondary cell which is discharged at a uniform rate of 30 A for 6 hr. at an average terminal voltage of 2 V. It is then charged at the uniform rate of 40 A for 5 hr. to restore it to its original condition. The terminal voltage during charging is 2.5 V.

## Short answer

Trickle charging maintains a standby battery at full charge by supplying a small continuous current equal to its self-discharge loss. For the given cell, ampere-hour efficiency is 90% (180 Ah discharged / 200 Ah charged) and watt-hour efficiency is 72% (360 Wh discharged / 500 Wh charged).

## Answer

#### Trickle charging
**Trickle charging** is the method of giving a battery that is not in use a **small, continuous charging current** just large enough to make up for its **self-discharge** (internal losses), so it always stays fully charged.
- The current is very small, about 1% of the Ah rating or less (e.g. about 1 A or less for a 100 Ah battery); a healthy lead-acid battery may need as little as about 1 mA per Ah.
- The charger is permanently connected; the battery does not supply the load in normal times.
- Used for standby batteries: emergency lighting, fire alarms, engine-starting batteries of DG sets and switchgear tripping batteries.
- Over-trickling causes gassing and water loss, so the current must be adjusted.

```text
 AC ─►[Transformer+Rectifier]─►[R]─► + Battery −
                  (small current)
```

#### Numerical
**Given:** discharge 30 A for 6 h at 2 V average; charge 40 A for 5 h at 2.5 V average.

**(i) Ampere-hour efficiency**
```text
Ah on discharge = 30 × 6 = 180 Ah
Ah on charge    = 40 × 5 = 200 Ah
η_Ah = 180 / 200 × 100 = 90 %
```

**(ii) Watt-hour efficiency**
```text
Wh on discharge = 180 × 2   = 360 Wh
Wh on charge    = 200 × 2.5 = 500 Wh
η_Wh = 360 / 500 × 100 = 72 %
```
(Check: η_Wh = η_Ah × V_dis/V_ch = 0.9 × 2/2.5 = 0.72.)

**Answer: Ampere-hour efficiency = 90 %, watt-hour efficiency = 72 %.**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What does trickle charging do?
   A. Charges a deeply discharged battery quickly
   B. Supplies the load in normal times
   C. Supplies a small continuous current to make up for self-discharge of an idle battery
   D. Equalises specific gravity across cells
   Answer: C. Trickle current is about 1-2% of Ah capacity and keeps standby batteries full. (Key point: Trickle charging purpose)

2. What is the Ah efficiency (discharge 30 A for 6 h, charge 40 A for 5 h)?
   A. 90%
   B. 72%
   C. 83%
   D. 111%
   Answer: A. 180 Ah / 200 Ah = 0.9. (Key point: Ampere-hour efficiency)

3. What is the Wh efficiency (2 V discharge, 2.5 V charge)?
   A. 90%
   B. 72%
   C. 80%
   D. 62.5%
   Answer: B. 360 Wh / 500 Wh = 72%, or 0.9 x 2/2.5. (Key point: Watt-hour efficiency)

4. Why is Wh efficiency lower than Ah efficiency?
   A. Charging current is lower than discharge current
   B. Discharge time is longer than charge time
   C. Ah are measured wrongly
   D. Charging voltage is higher than discharge voltage
   Answer: D. Wh = Ah x V; the cell is charged at 2.5 V but delivers at 2 V, so efficiency drops by the voltage ratio. (Key point: Why Wh efficiency is lower)

## Related in Industrial Power Distribution and Illumination

- [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×
- [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×
- [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