---
title: "Load factor and demand factor numerical"
subject: "Industrial Power Distribution and Illumination"
chapter: 1
key: "semester_6/industrial_power_distribution_and_illumination:consumer-load-demand-factor"
source: https://www.bctengineer.com/q/semester_6/industrial_power_distribution_and_illumination/consumer-load-demand-factor
site: BCT Engineering
---

# Load factor and demand factor numerical

Industrial Power Distribution and Illumination · Chapter 1: Introduction

- Asked in: 2075 Baisakh, 4 marks
- Video: [Load Factor, Diversity Factor, Plant Capacity Factor, Utilization Factor, Reserve Capacity](https://www.youtube.com/watch?v=CeVFXs6mnUU) — Electrical Minus
- 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/consumer-load-demand-factor
- Whole chapter: https://www.bctengineer.com/md/semester_6/industrial_power_distribution_and_illumination/chapter-1

## Question

A consumer has the following connected loads: 12 lamps of 80 W each and 4 heaters of 100 W each. His maximum demand is 1500 W. On the average consumer uses 8 lamps 6 hours a day and each heater for 4 hours a day. Find load factor and demand factor.

## Short answer

Connected load = 1360 W (12×80W lamps + 4×100W heaters). Daily energy = 5440 Wh (8 lamps×6h + 4 heaters×4h). Average load = 226.67 W. Demand factor = 1500/1360 = 1.103; load factor = 226.67/1500 = 0.151 (15.1%). Note: demand factor >1 indicates probable heater rating error (should be 1000W).

## Answer

**Formulas used**

```text
Demand factor = Maximum demand / Connected load
Load factor   = Average load / Maximum demand
Average load  = Energy per day / 24 h
```

#### Connected load
```text
Lamps   : 12 × 80 W  =  960 W
Heaters :  4 × 100 W =  400 W
Connected load       = 1360 W
```

#### Daily energy and average load
```text
Lamps   : 8 × 80 W × 6 h  = 3840 Wh
Heaters : 4 × 100 W × 4 h = 1600 Wh
Energy per day            = 5440 Wh
Average load = 5440 / 24  = 226.67 W
```

#### Factors
```text
Demand factor = 1500 / 1360   = 1.103
Load factor   = 226.67 / 1500 = 0.1511
```

**Answer (data as printed): load factor = 0.151 (15.1%), demand factor = 1.10.**

**Note on the data:** a demand factor greater than 1 is not possible, because the maximum demand cannot exceed the connected load. The heater rating is almost certainly **1000 W** (the standard textbook version of this problem). With 4 heaters of 1000 W:

```text
Connected load = 960 + 4000           = 4960 W
Energy/day = 3840 + 4×1000×4          = 19840 Wh
Average load = 19840 / 24             = 826.67 W
Demand factor = 1500 / 4960           = 0.3024
Load factor   = 826.67 / 1500         = 0.5511
```

**Answer (heaters 1000 W): demand factor = 0.302, load factor = 0.551 (55.1%).**

## Check yourself

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

1. What is the demand factor?
   A. Average load / maximum demand
   B. Maximum demand / connected load
   C. Connected load / maximum demand
   D. Sum of individual MDs / system MD
   Answer: B. Demand factor compares maximum demand with total connected load. (Key point: Demand factor formula)

2. What is the connected load for 12 lamps of 80 W and 4 heaters of 100 W?
   A. 1360 W
   B. 1500 W
   C. 960 W
   D. 5440 W
   Answer: A. 12 x 80 + 4 x 100 = 960 + 400 = 1360 W. (Key point: Connected load)

3. What is the average load for 8 lamps for 6 h and 4 heaters of 100 W for 4 h?
   A. 5440 W
   B. 1360 W
   C. 453.3 W
   D. 226.67 W
   Answer: D. Energy = 3840 + 1600 = 5440 Wh, divided by 24 h = 226.67 W. (Key point: Average load)

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