---
title: "BMS functions and EV range numerical"
subject: "Automotive Technology"
chapter: 12
key: "semester_5/automotive_technology:bms-ev-range-numerical"
source: https://www.bctengineer.com/q/semester_5/automotive_technology/bms-ev-range-numerical
site: BCT Engineering
---

# BMS functions and EV range numerical

Automotive Technology · Chapter 12: Trends in Automobiles

- Asked in: year not given, 3+4 marks
- Video: [What is a Battery Management System? | Topologies of the BMS](https://www.youtube.com/watch?v=KDaBn9PLRKI) — Foolish Engineer
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/automotive_technology/bms-ev-range-numerical
- Whole chapter: https://www.bctengineer.com/md/semester_5/automotive_technology/chapter-12

## Question

(a) State the main functions of a battery management system (BMS). (b) An electric car has a 40 kWh battery of which 90 % is usable and consumes 160 Wh/km. Find its range. It is charged from 20 % to 80 % of the 40 kWh capacity through an AC charger of 7.4 kW rated output with 92 % efficiency. Find the charging time.

## Short answer

BMS monitors cell voltage/temp, estimates SoC/SoH, protects against overcharge/discharge, balances cells, manages thermal. Usable energy 0.9×40=36 kWh, range 36000/160=225 km. Charging energy (0.8-0.2)×40=24 kWh; effective power 7.4×0.92=6.81 kW; time 24/6.81≈3.53 h (3 h 32 min).

## Answer

#### (a) Functions of a BMS

1. **Monitoring** of cell voltages, pack current and temperature.
2. **State of charge (SoC)** and **state of health (SoH)** estimation.
3. **Protection** against over-charge, deep discharge, over-current, short circuit and over-temperature, by tripping the contactors.
4. **Cell balancing** (passive, using resistors, or active, by transferring charge), so that all cells have the same SoC.
5. **Thermal management:** control of cooling or heating.
6. **Communication** with the vehicle ECU and the charger over CAN, including limits on charge and discharge power.

#### (b) Numerical

**Range**

$$
E_{usable} = 0.9 \times 40 = 36\ \text{kWh}, \qquad \text{Range} = \frac{36\,000}{160} = 225\ \text{km}
$$

**Charging time**

Energy to be stored $= (0.80 - 0.20) \times 40 = 24$ kWh.

Taking 7.4 kW as the AC power the charger supplies and 92 % as the charging efficiency, the power reaching the battery is:

$$
P_{eff} = 7.4 \times 0.92 = 6.81\ \text{kW}, \qquad t = \frac{24}{6.81} = 3.53\ \text{h}
$$

The energy drawn from the supply is $24/0.92 = 26.1$ kWh. (If instead the full 7.4 kW reached the battery, the time would be $24/7.4 = 3.24$ h. In practice the charging rate tapers near 80 % SoC.)

**Answer:** range $= 225$ km; charging time $\approx 3.53$ h (3 h 32 min).

## Check yourself

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

1. What is cell balancing?
   A. Measuring current
   B. Cooling cells
   C. Raising voltage
   D. Equalising SoC of all cells by resistors (passive) or charge transfer (active)
   Answer: D. Balancing keeps cells at the same state of charge. (Key point: Cell balancing)

2. Which are BMS protection functions?
   A. Over-charge, deep discharge, over-current, short circuit and over-temperature
   B. Wheel lock
   C. Tyre pressure only
   D. Steering
   Answer: A. The BMS trips the contactor on faults. (Key point: Protection)

3. Range of a 40 kWh battery, 90 % usable, at 160 Wh/km?
   A. 250 km
   B. 160 km
   C. 225 km
   D. 36 km
   Answer: C. 36000/160 = 225 km. (Key point: Range)

4. Time to charge 20 % to 80 % of 40 kWh with 7.4 kW at 92 % efficiency?
   A. 5.4 h
   B. 2.0 h
   C. 3.24 h
   D. 3.53 h
   Answer: D. 24 kWh / (7.4 x 0.92 = 6.81 kW) = 3.53 h. (Key point: Charging time)

## Related in Automotive Technology

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- [Electric vehicle architecture and traction motors](https://www.bctengineer.com/question.md?key=semester_5%2Fautomotive_technology%3Aev-architecture-and-motors) — Automotive Technology, chapter 12
- [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

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