Analyzing Electricity Capacity Growth: State X vs State Y

The question asks us to determine which state and which energy source showed the maximum percentage decadal growth in installed electricity capacity between the years 2011 and 2021. To answer this, we need to calculate the percentage growth for Solar, Wind, and Coal capacities in both State X and State Y over this decade.

The data provided is in the following table:

The formula for calculating the percentage decadal growth is:

Percentage Growth (%) $= \left( \frac{\text{Capacity in 2021} - \text{Capacity in 2011}}{\text{Capacity in 2011}} \right) \times 100$

Let's calculate the percentage growth for each energy source in both states.

Calculating Percentage Decadal Growth

State X

• Solar:

  Capacity in 2011 = 20 GW, Capacity in 2021 = 28 GW

  Percentage Growth $= \left( \frac{28 - 20}{20} \right) \times 100 = \left( \frac{8}{20} \right) \times 100 = 0.4 \times 100 = 40\%$

• Wind:

  Capacity in 2011 = 10 GW, Capacity in 2021 = 15 GW

  Percentage Growth $= \left( \frac{15 - 10}{10} \right) \times 100 = \left( \frac{5}{10} \right) \times 100 = 0.5 \times 100 = 50\%$

• Coal:

  Capacity in 2011 = 40 GW, Capacity in 2021 = 42 GW

  Percentage Growth $= \left( \frac{42 - 40}{40} \right) \times 100 = \left( \frac{2}{40} \right) \times 100 = 0.05 \times 100 = 5\%$

State Y

• Solar:

  Capacity in 2011 = 15 GW, Capacity in 2021 = 20 GW

  Percentage Growth $= \left( \frac{20 - 15}{15} \right) \times 100 = \left( \frac{5}{15} \right) \times 100 \approx 0.3333 \times 100 \approx 33.33\%$

• Wind:

  Capacity in 2011 = 0 GW, Capacity in 2021 = 5 GW

  Percentage Growth $= \left( \frac{5 - 0}{0} \right) \times 100$. This calculation involves division by zero, which is undefined. However, we can see there was a significant absolute increase from 0 to 5 GW. When comparing percentage growths calculated from a non-zero base, this case is usually considered separately or the absolute growth is noted. In the context of MCQs with calculated options, we compare the valid percentages.

• Coal:

  Capacity in 2011 = 50 GW, Capacity in 2021 = 55 GW

  Percentage Growth $= \left( \frac{55 - 50}{50} \right) \times 100 = \left( \frac{5}{50} \right) \times 100 = 0.1 \times 100 = 10\%$

Summary of Percentage Decadal Growth

Let's list the calculated percentage growth values:

• State X, Solar: 40%
• State X, Wind: 50%
• State X, Coal: 5%
• State Y, Solar: ≈ 33.33%
• State Y, Wind: Growth from 0 (Undefined Percentage)
• State Y, Coal: 10%

Comparing the valid percentage growth values (40%, 50%, 5%, 33.33%, 10%), the maximum percentage decadal growth is 50%. This occurred in State X for Wind energy. Although State Y Wind grew from 0, which represents a substantial increase, the standard percentage growth calculation is undefined. Based on the calculable percentages, State X Wind shows the highest growth.

Conclusion

The maximum percentage decadal growth in installed capacity was in State X for Wind energy, with a growth of 50%.

Revision Table: Electricity Capacity Analysis

Additional Information: Understanding Energy Capacity Growth

Analyzing the growth of installed electricity capacity is crucial for understanding a region's transition towards different energy sources, especially renewable ones like solar and wind.

• Installed Capacity: This refers to the maximum output an electricity generation facility can produce under specific conditions. It indicates the potential power supply from a source.
• Decadal Growth: Measuring changes over a decade (10 years) provides insights into longer-term trends in energy infrastructure development.
• Percentage Growth Calculation: The formula used is standard for measuring relative change. However, calculating percentage change is not suitable when the base value (starting point) is zero, as division by zero is mathematically undefined. In such cases, absolute growth (the difference between the final and initial value) or other metrics are used.
• Types of Energy Sources:
  • Solar Power: Electricity generated from sunlight using photovoltaic panels or solar thermal systems.
  • Wind Power: Electricity generated from wind using wind turbines.
  • Coal Power: Electricity generated by burning coal to heat water, produce steam, and drive turbines. Coal is a traditional, non-renewable source.
• Growth Trends: Often, renewable energy sources like solar and wind show high percentage growth, especially from a low base, reflecting investments in clean energy. Coal capacity growth might be slower or even negative as regions shift towards renewables.