Sources of Energy in the World

Lessons

Senior 4 · Physics

Sources of Energy in the World

4 lessons

Lesson 1 of 4

Energy and the World's Energy Sources

25 min

A planet seen at night

Satellites that photograph the Earth at night show where people use energy. Western Europe glitters; the Nile valley is a bright thread through dark desert; much of Africa between the Sahara and South Africa is almost black, because few homes and streets there have electric light. The pattern is not about how many people live in a place. It is about how much energy each of them can use. In S3 you classified Rwanda's sources of electricity as renewable or non-renewable. In this lesson you measure energy and power properly, trace every source back to where its energy first came from, and read the world's and Rwanda's energy mix with numbers.

Energy, power and their units

Energy is what is transferred when a force does work or when a hotter body heats a cooler one. It is conserved: it can change from one form to another (kinetic, gravitational potential, elastic, chemical, nuclear, internal, electrical, radiant) but the total never changes. A society "uses up" energy only in the sense that it turns useful forms, such as the chemical energy of diesel, into spread-out internal energy of the surroundings, which can no longer do much work.

The SI unit of energy is the joule (J). Electricity companies sell energy in kilowatt-hours, and national statistics use gigawatt-hours (GWh) and terawatt-hours (TWh):

1\,\mathrm{kWh} = 1000\,\mathrm{W} \times 3600\,\mathrm{s} = 3.6 \times 10^{6}\,\mathrm{J}, \qquad 1\,\mathrm{TWh} = 10^{9}\,\mathrm{kWh} = 3.6 \times 10^{15}\,\mathrm{J}

Power is the rate of transferring energy, $P = \frac{E}{t}$ , in watts ( $1\,\mathrm{W} = 1\,\mathrm{J\,s^{-1}}$ ). A power station is rated by its power (MW); a country's yearly use is an energy (GWh or TWh). Dividing one by the other gives a time, which is how the two are connected.

Definition

Energy $E$ is the capacity to do work, measured in joules (J); 1 kWh = $3.6 \times 10^{6}$ J. Power $P$ is the rate at which energy is transferred, $P = \frac{E}{t}$ , measured in watts (W). Example: a 2.0 kW kettle that runs for 3.0 minutes transfers $2000 \times 180 = 3.6 \times 10^{5}\,\mathrm{J} = 0.10\,\mathrm{kWh}$ .

Why energy matters

Every activity of a modern economy needs a steady flow of energy: cooking and heating water, lighting homes and streets so that pupils can study after dark, pumping and treating water, keeping vaccines cold in health centres, running mobile networks and computers, milling grain, moving goods and people, and making cement, steel and fertiliser. Across countries, the energy used per person rises with income, life expectancy and years of schooling. Energy is not the only cause of development, but no country has become rich while its people used very little of it.

Rwanda's demand is growing fast. Rwanda Energy Group's Least Cost Power Development Plan, 2024 Review (REG, September 2025) records a national electricity demand of 0.690 TWh in 2016 and 1.477 TWh in 2024, with a peak demand (the largest power drawn at any moment) of 242 MW in 2024. NISR's survey EICV7 found that the share of households using electricity for lighting rose from 34% in 2016–17 to 72% in 2023–24.

Worked example 1: average power and load factor of the national grid

In 2024 Rwanda's electricity demand was 1.477 TWh and its peak demand 242 MW (REG, 2025). Find the average power drawn over the year and the ratio of average to peak power.

One year is $365 \times 24 = 8760\,\mathrm{h}$ .

P_{\text{av}} = \frac{E}{t} = \frac{1.477 \times 10^{12}\,\mathrm{Wh}}{8760\,\mathrm{h}} = 1.686 \times 10^{8}\,\mathrm{W} \approx 169\,\mathrm{MW}

\text{load factor} = \frac{P_{\text{av}}}{P_{\text{peak}}} = \frac{168.6\,\mathrm{MW}}{242\,\mathrm{MW}} = 0.697 \approx 70\%

The grid must be able to supply 242 MW in the evening peak, even though it supplies only 169 MW on average. Plants that can start quickly are needed for the remaining 30%: this is why REG keeps diesel units for peak hours.

Worked example 2: electricity per person

The 2022 census counted 13 246 394 people in Rwanda (NISR). Taking 13.2 million as the population and the 2024 demand of 1.477 TWh, estimate the electricity used per person per year, and the average power per person.

\frac{1.477 \times 10^{9}\,\mathrm{kWh}}{1.32 \times 10^{7}} = 112\,\mathrm{kWh} \text{ per person per year}

P = \frac{112 \times 3.6 \times 10^{6}\,\mathrm{J}}{3.156 \times 10^{7}\,\mathrm{s}} = 12.8\,\mathrm{W}

That is the average power of one small LED bulb per person, running day and night. The population figure is two years older than the demand, so the answer is a slight overestimate; one significant figure more would be false precision.

Where energy sources come from

A primary energy source is energy as it is found in nature: sunlight, wind, flowing water, wood, coal, crude oil, natural gas, uranium, the Earth's heat. Electricity, petrol, charcoal and hydrogen are secondary forms (energy carriers): they are made from primary sources, with some loss, and are used because they are easy to move and control. Electricity is never a source of energy in itself.

Almost every source can be traced back to one of four origins (Figure 1.1). Most come from nuclear fusion in the Sun: sunlight directly; wind, because the Sun heats the ground unevenly; hydroelectric power, because sunlight evaporates water that later falls as rain on high ground; biomass, through photosynthesis; and fossil fuels, which are the remains of plants and plankton buried and compressed over millions of years. Geothermal energy comes from the Earth's interior, kept hot largely by radioactive decay; tides come from the gravity of the Moon and Sun; and nuclear power uses uranium that was formed in stars that exploded before the Sun was born.

Figure 1.1: Every energy source traced to its origin. Solid borders: renewable; dashed borders: non-renewable.

Definition

A renewable energy source is one that is replaced by natural processes at least as fast as it is used: solar, wind, hydroelectric, geothermal, tidal, and biomass that is regrown. A non-renewable energy source is a stock that took millions of years to form, or cannot form again on Earth, so using it reduces what is left: coal, oil, natural gas, peat and uranium. Example: firewood from a woodlot that is replanted is renewable; cutting a natural forest faster than it regrows uses the forest like a non-renewable stock.

The world's energy mix and Rwanda's

Figure 1.2 shows how the world's primary energy was supplied in 2025. Fossil fuels still gave about 86%, even though solar and wind are the fastest-growing sources. The chart counts all uses of energy: transport, industry and heating as well as electricity.

Figure 1.2: World primary energy by source, 2025. Data: Our World in Data, from the Energy Institute Statistical Review of World Energy (2026).

Rwanda's picture is very different. Most of its primary energy is biomass used for cooking: in 2023–24 firewood was the main cooking fuel of 92.5% of rural households, and 51% of urban households cooked with charcoal (NISR, EICV7). Its electricity, a much smaller part of total energy, came from the sources in Table 1.1.

Source of Rwanda's electricity	Renewable?	Share of generation, 2024
hydropower	yes	35%
methane gas from Lake Kivu	no	35%
imports and regionally shared plants	counted as renewable by REG	20%
peat	no	8%
solar	yes	1.2%
diesel and heavy fuel oil (thermal)	no	1%

Table 1.1: Rwanda's electricity generation mix. Source: REG, Least Cost Power Development Plan, 2024 Review (September 2025), Figure 6, which puts the renewable share at 56.21%. Installed capacity serving the grid was 466 MW.

Worked example 3: how long will a reserve last?

A gas field holds an estimated $2.0 \times 10^{10}\,\mathrm{m^3}$ of gas, and $5.0 \times 10^{8}\,\mathrm{m^3}$ is extracted this year (illustrative figures). (a) How long would it last at this rate? (b) How long if extraction grows by 5.0% a year?

(a) The reserves-to-production ratio is $\frac{2.0 \times 10^{10}}{5.0 \times 10^{8}} = 40$ years.

(b) With growth, the total extracted in $n$ years is a geometric series:

P_0\,\frac{1.05^{\,n} - 1}{0.05} = R \;\Rightarrow\; 1.05^{\,n} = 1 + \frac{0.05 \times 2.0 \times 10^{10}}{5.0 \times 10^{8}} = 3.0

n = \frac{\ln 3.0}{\ln 1.05} = 22.5 \approx 23 \text{ years}

Modest growth in use almost halves the lifetime. A fixed stock looks large until the rate of use keeps rising.

Warning

Common mistakes. (1) Mixing up power (kW, MW) and energy (kWh, GWh): a 242 MW peak is not "242 MW per year". (2) Calling electricity a source: it is a carrier made from a primary source. (3) Thinking renewable means clean: burning wood is renewable if it is regrown, yet its smoke harms health. (4) Comparing a country's electricity mix with the world's primary-energy mix: they measure different things.

Tip

Units first. Before any energy calculation, turn every quantity into joules and seconds, or every quantity into kWh and hours, and do not mix the two. Remember $1\,\mathrm{year} = 8760\,\mathrm{h} = 3.156 \times 10^{7}\,\mathrm{s}$ .

Renewable Energy 101 (National Geographic). Watch for how each renewable source is traced back to the Sun, the Earth's heat or the Moon, as in Figure 1.1, and for the drawbacks of each source mentioned at the end.

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Practice

Convert (a) 5.0 kWh to joules; (b) $7.2 \times 10^{9}$ J to kWh; (c) 1.477 TWh to joules.
Classify each as a primary source or a secondary form of energy, and each primary source as renewable or non-renewable: charcoal, peat, sunlight, electricity, methane from Lake Kivu, petrol, geothermal heat.
A 3.6 MW solar plant produces 6.3 GWh in a year. Find its average power output, and the ratio of average power to rated power.
Rwanda's demand was 0.690 TWh in 2016 and 1.477 TWh in 2024 (REG, 2025). Find the average yearly growth rate over those 8 years.
Explain why wind energy and fossil fuels can both be said to come from the Sun, yet only one of them is renewable.
Using Figure 1.2, find the ratio of fossil-fuel energy to renewable energy in the world's 2025 mix, and comment on what it means for how quickly the world can stop using fossil fuels.
A reserve of 600 units is used at 15 units in the first year, and use grows by 3.0% each year. Find how long it lasts, and compare with the reserves-to-production ratio.
A classmate says: "Rwanda already gets 56% of its energy from renewables, so it has almost finished its energy transition." Evaluate this statement using the data in this lesson.

Show answersHide answers

(a) $5.0 \times 3.6 \times 10^{6} = 1.8 \times 10^{7}\,\mathrm{J}$ ; (b) $\frac{7.2 \times 10^{9}}{3.6 \times 10^{6}} = 2.0 \times 10^{3}\,\mathrm{kWh}$ ; (c) $1.477 \times 10^{9} \times 3.6 \times 10^{6} = 5.32 \times 10^{15}\,\mathrm{J}$ .
Primary: peat (non-renewable), sunlight (renewable), methane (non-renewable), geothermal heat (renewable). Secondary: charcoal, electricity, petrol.
$P_{\text{av}} = \frac{6.3 \times 10^{9}\,\mathrm{Wh}}{8760\,\mathrm{h}} = 7.2 \times 10^{5}\,\mathrm{W} = 0.72\,\mathrm{MW}$ ; ratio $\frac{0.72}{3.6} = 0.20$ , or 20%.
$\left(\frac{1.477}{0.690}\right)^{\frac{1}{8}} = 2.141^{0.125} = 1.100$ : about 10% a year.
Wind is driven by the Sun's uneven heating today and is replaced continuously; fossil fuels are sunlight stored by plants millions of years ago, and the stock forms far more slowly than it is used.
$\frac{86.2}{8.5} \approx 10$ : fossil fuels supply about ten times as much energy as renewables. Even fast-growing renewables must grow many times over, while total demand also rises, so the change will take decades.
$15\,\frac{1.03^{n} - 1}{0.03} = 600 \Rightarrow 1.03^{n} = 2.2 \Rightarrow n = \frac{\ln 2.2}{\ln 1.03} = 26.7$ years, against a reserves-to-production ratio of $\frac{600}{15} = 40$ years.
The 56% is REG's renewable share of electricity generation in 2024. Electricity is a small part of Rwanda's total energy, most of which is biomass for cooking (92.5% of rural households cook mainly with firewood, NISR 2023–24), and wood is renewable only if it is replanted. Transport runs on imported petroleum. So the electricity mix is fairly renewable, but the energy system as a whole still has a long way to go.

Quick check

Rwanda's 2024 peak demand was 242 MW. Which statement about this number is correct?

Key points

Energy (J, kWh) is conserved; power $P = \frac{E}{t}$ (W) is its rate of transfer; $1\,\mathrm{kWh} = 3.6 \times 10^{6}\,\mathrm{J}$ .
Primary sources are found in nature; electricity, petrol and charcoal are secondary carriers.
Renewable sources are replaced as fast as they are used; fossil fuels, peat and uranium are not. Most sources trace back to the Sun.
Fossil fuels gave about 86% of world primary energy in 2025; 56% of Rwanda's electricity came from renewables in 2024, but most of its total energy is wood for cooking.

Sources and credits

7.9: World Energy Use, from College Physics (1st edition) by Paul Peter Urone and Roger Hinrichs, OpenStax, hosted by LibreTexts, licensed under CC BY 4.0. Adapted by Ganzaa.
World data: Share of primary energy use by source, Our World in Data, from the Energy Institute Statistical Review of World Energy (2026), licensed under CC BY 4.0; chart redrawn by Ganzaa.
Rwandan facts: Rwanda Energy Group, Rwanda Least Cost Power Development Plan, 2024 Review (September 2025), Table 2 and Figure 6; National Institute of Statistics of Rwanda, EICV7 Thematic Report: Utilities and Amenities 2023–24 and Fifth Population and Housing Census 2022: Main Indicators.
Photo: City Lights of Africa, Europe, and the Middle East by NASA Earth Observatory (Robert Simmon), Wikimedia Commons, public domain.
Video: Renewable Energy 101, National Geographic, embedded from YouTube.

The diagrams, table, worked examples and practice exercises are written by Ganzaa.

1A planet seen at night

2Energy, power and their units

3Why energy matters

4Where energy sources come from

5The world's energy mix and Rwanda's

A planet seen at night

Energy, power and their units

Why energy matters

Where energy sources come from

The world's energy mix and Rwanda's