---
title: "Battery fundamentals and battery bank sizing"
subject: "Energy Resources"
chapter: 6
key: "semester_6/energy_resources:battery-fundamentals-sizing"
source: https://www.bctengineer.com/q/semester_6/energy_resources/battery-fundamentals-sizing
site: BCT Engineering
---

# Battery fundamentals and battery bank sizing

Energy Resources · Chapter 6: Non conventional forms of energy and batteries

- Asked in: year not given, 4+4 marks
- Video: [Sizing Battery Capacity For Your Solar Power System - The Basics (Ep. 4)](https://www.youtube.com/watch?v=wuqbRUrlv-s) — The Solar Lab
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/energy_resources/battery-fundamentals-sizing
- Whole chapter: https://www.bctengineer.com/md/semester_6/energy_resources/chapter-6

## Question

(a) Define primary and secondary cells. Explain the terms capacity, C-rate, depth of discharge and energy density. Compare lead-acid and lithium-ion batteries. (b) A stand-alone solar home system has a daily load of 1.2 kWh. The battery bank at 12 V must supply the load for 2 days without sun. The allowed depth of discharge is 50 % and the battery round-trip efficiency is 85 %. Find the required capacity in Ah.

## Short answer

Primary cells are non-rechargeable; secondary are rechargeable. Capacity (Ah), C-rate (current/capacity), DoD (fraction used), energy density (Wh/kg). Lead-acid: 2V, 30-50 Wh/kg, low cost; Li-ion: 3.6-3.7V, 150-250 Wh/kg, longer life. Required capacity: (1.2×2)/(0.5×0.85×12) = 471 Ah at 12 V.

## Answer

#### (a) Battery fundamentals
- **Primary cell:** chemical reaction is irreversible; used once and thrown away (zinc-carbon, alkaline).
- **Secondary cell:** reaction can be reversed by passing charging current; rechargeable (lead-acid, Ni-Cd, Ni-MH, Li-ion).

**Terms**
- **Capacity (Ah):** charge a battery can deliver at a specified rate from full to cut-off voltage. Energy = capacity × voltage (Wh).
- **C-rate:** discharge current expressed as a multiple of capacity; 1C for a 100 Ah battery is 100 A, 0.1C is 10 A.
- **Depth of discharge (DoD):** percentage of capacity used. Deeper discharge shortens life.
- **Energy density:** energy stored per unit mass (Wh/kg) or volume (Wh/L).

| Point | Lead-acid | Lithium-ion |
|---|---|---|
| Cell voltage | 2.0 V | 3.6–3.7 V |
| Energy density | 30–50 Wh/kg | 150–250 Wh/kg |
| Cycle life | 300–1000 (at 50 % DoD) | 1000–5000 |
| Usable DoD | 50 % | 80–90 % |
| Efficiency | 80–85 % | 95 % |
| Cost per kWh | Low | Higher, falling |
| Maintenance | Water topping (flooded type) | Needs battery management system |

#### (b) Battery bank sizing
Energy to be stored (autonomy): $1.2 \times 2 = 2.4$ kWh = 2400 Wh.

$$
C = \frac{E \times \text{days}}{DoD \times \eta \times V} = \frac{1200 \times 2}{0.50 \times 0.85 \times 12} = \frac{2400}{5.1} = 470.6\ \text{Ah}
$$

**Answer:** about 471 Ah at 12 V, so a bank of 500 Ah (for example, five 100 Ah, 12 V batteries in parallel) is selected.

## Check yourself

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

1. What distinguishes a secondary cell from a primary cell?
   A. Its reaction can be reversed by charging, so it is rechargeable
   B. It is used once and discarded
   C. It has no electrolyte
   D. It always has higher voltage
   Answer: A. Secondary cells (lead-acid, Li-ion) are rechargeable; primary cells (zinc-carbon) are not. (Key point: Primary vs secondary cell)

2. What is a discharge current of 0.1C for a 100 Ah battery?
   A. 100 A
   B. 1 A
   C. 10 A
   D. 0.1 A
   Answer: C. C-rate is a multiple of capacity: 0.1 x 100 = 10 A. (Key point: C-rate)

3. How does lithium-ion compare with lead-acid?
   A. Lower energy density and shorter life
   B. Higher energy density (150-250 Wh/kg), longer cycle life and deeper usable DoD
   C. Lower cell voltage of 2 V
   D. Needs water topping
   Answer: B. Li-ion is better in energy density, cycle life, DoD and efficiency, but costs more and needs a BMS. (Key point: Lead-acid vs Li-ion)

4. Which formula sizes the bank for 2 days of autonomy?
   A. C = 1200 x 2 / (0.5 x 0.85 x 12) = 471 Ah
   B. C = 1200 x 2 x 0.5 x 0.85 / 12
   C. C = 1200 / (12 x 2)
   D. C = 1200 x 2 / 12 = 200 Ah
   Answer: A. Stored energy is divided by DoD, efficiency and voltage, since only part of the capacity is usable and some energy is lost. (Key point: Battery bank sizing)

## Related in Energy Resources

- [Working principle and types of fuel cells](https://www.bctengineer.com/question.md?key=semester_6%2Fenergy_resources%3Apem-fuel-cell-working-types) — Energy Resources, chapter 6
- [Solar concentrators and concentration ratio](https://www.bctengineer.com/question.md?key=semester_6%2Fenergy_resources%3Asolar-concentrators-types-concentration-ratio) — Energy Resources, chapter 2
- [Earth's motion, solar constant and seasons](https://www.bctengineer.com/question.md?key=semester_6%2Fenergy_resources%3Aearth-sun-geometry-solar-constant) — Energy Resources, chapter 2
- [Solar angles for a site in Nepal](https://www.bctengineer.com/question.md?key=semester_6%2Fenergy_resources%3Asolar-angles-kathmandu-calculation) — Energy Resources, chapter 2
- [Flat plate collector and solar water heater](https://www.bctengineer.com/question.md?key=semester_6%2Fenergy_resources%3Aflat-plate-collector-construction-water-heater) — Energy Resources, chapter 2
- [Sizing a family biogas plant](https://www.bctengineer.com/question.md?key=semester_6%2Fenergy_resources%3Abiogas-plant-sizing-cattle-dung) — Energy Resources, chapter 3

## Related in other subjects

- [Lead-acid battery construction and rating](https://www.bctengineer.com/question.md?key=semester_5%2Fautomotive_technology%3Alead-acid-battery-construction-rating) — Automotive Technology, 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
- [Primary and secondary energy (102 m head)](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Aprimary-secondary-energy-102m) — Hydro Power, chapter 3
- [Primary/secondary energy and pondage volume](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Aenergy-and-pondage-volume) — Hydro Power, chapter 3