Understanding Per Capita Electricity Availability

The question asks us to calculate the per capita availability of electricity in State X for the year 2021. Per capita availability means the amount of a resource (in this case, electricity generation capacity) available per person in a given population. To find this, we need two key pieces of information from the provided table:

1. The total installed capacity of electricity generation in State X in 2021.
2. The population of State X in 2021.

Extracting Data for State X in 2021

Let's look at the data provided for State X in the year 2021:

From this table, we gather the following data for State X in 2021:

• Population: 60 million (mn)
• Installed Solar Capacity: 28 GW
• Installed Wind Capacity: 15 GW
• Installed Coal Capacity: 42 GW

Calculating Total Installed Capacity in State X (2021)

The total installed capacity is the sum of the capacities from all listed sources (Solar, Wind, and Coal) in State X for the year 2021.

Total Installed Capacity (GW) = Solar Capacity + Wind Capacity + Coal Capacity

Total Installed Capacity (GW) = \(28 \text{ GW} + 15 \text{ GW} + 42 \text{ GW}\)

Total Installed Capacity (GW) = \(85 \text{ GW}\)

Converting Units for Per Capita Calculation

The question asks for per capita availability in kilowatts (kW). The total installed capacity is currently in gigawatts (GW), and the population is in millions (mn).

We need to convert GW to kW and million people to the total number of people.

• 1 GW = \(10^6\) kW (1 Gigawatt = 1,000,000 kilowatts)
• 1 million = \(10^6\)

Total Installed Capacity in kW = \(85 \text{ GW} \times 10^6 \text{ kW/GW} = 85 \times 10^6 \text{ kW}\)

Population in 2021 = \(60 \text{ mn} = 60 \times 10^6 \text{ people}\)

Calculating Per Capita Availability of Electricity

Now we can calculate the per capita availability of electricity in kW by dividing the total installed capacity in kW by the total population.

Per Capita Availability (kW/person) = \(\frac{\text{Total Installed Capacity (kW)}}{\text{Population (people)}}\)

Per Capita Availability (kW/person) = \(\frac{85 \times 10^6 \text{ kW}}{60 \times 10^6 \text{ people}}\)

Notice that the \(10^6\) terms cancel out, simplifying the calculation:

Per Capita Availability (kW/person) = \(\frac{85}{60} \text{ kW/person}\)

Now, we perform the division:

\(\frac{85}{60} = \frac{17 \times 5}{12 \times 5} = \frac{17}{12}\)

\(\frac{17}{12} \approx 1.4166...\)

Rounding to two decimal places, this is approximately 1.42 kW/person. However, the options provided are rounded to different decimal places. Let's check the options against the calculated value \(\approx 1.4166...\).

• Option 1: \(\sim 1.21 \text{ kW}\) (Not close)
• Option 2: \(\sim 1.41 \text{ kW}\) (Very close to 1.4166...)
• Option 3: \(\sim 1.25 \text{ kW}\) (Not close)
• Option 4: \(\sim 1.62 \text{ kW}\) (Not close)

The calculated value \(1.4166...\) is closest to \(1.41\).

Therefore, the per capita availability of electricity in State X in the year 2021 was approximately 1.41 kW.

Summary of Calculation Steps

1. Identify the required data (Total Installed Capacity and Population for State X in 2021).
2. Sum up the installed capacities from all sources to get the total capacity in GW.
3. Convert total capacity from GW to kW.
4. Convert population from millions to the total number of people.
5. Divide the total capacity in kW by the total population to find the per capita availability in kW per person.
6. Compare the calculated value with the given options.

Revision Table: Key Data Points

Additional Information: Energy Capacity and Per Capita Metrics

Installed Capacity: This refers to the maximum power output that a power plant or set of power plants can produce under specific conditions. It's a measure of potential generation, not necessarily actual electricity generated over a period (which is measured in kWh or GWh).

Per Capita Availability: This metric helps understand the potential access to electricity for each individual in a population based on the installed capacity. Higher per capita installed capacity often correlates with higher electricity consumption and potentially a higher standard of living, although factors like grid infrastructure and actual generation/demand play crucial roles.

Units:

• Watt (W): Basic unit of power.
• Kilowatt (kW): 1 kW = 1,000 W = \(10^3\) W
• Megawatt (MW): 1 MW = 1,000 kW = \(10^6\) W
• Gigawatt (GW): 1 GW = 1,000 MW = \(10^9\) W

Converting between units is essential for calculations involving different scales of energy capacity.