E = I × A × t
Unit conversions to memorise: Always convert kW → W (multiply by 1000) and hours → seconds (multiply by 3600) before substituting into the formula.
Rearrangements
E = I × A × t
I = E / (A × t)
A = E / (I × t)
t = E / (I × A)
Solar Constant
The solar constant is approximately 1.4 kW/m² — the average solar energy received per second on 1 m² at the top of Earth's atmosphere when facing the Sun directly. At Earth's surface it is ~1 kW/m² due to atmospheric absorption.
Step-by-step solutions
A solar panel of area 3 m² is exposed to sunlight for 2 hours. If insolation is 1 kW/m², how much energy does it receive?
Write given values: I = 1 kW/m², A = 3 m², t = 2 hours
Convert units: I = 1000 W/m², t = 2 × 3600 = 7200 s
Apply formula: E = I × A × t = 1000 × 3 × 7200
E = 21,600,000 J = 2.16 × 10⁷ J
A surface receives 5.4 × 10⁶ J in 30 minutes. If insolation is 1 kW/m², what is the area?
Given: E = 5,400,000 J, I = 1000 W/m², t = 30 min = 1800 s
Rearrange: A = E / (I × t)
Substitute: A = 5,400,000 / (1000 × 1800) = 5,400,000 / 1,800,000
A = 3 m²
How long must a 4 m² panel be exposed to 1 kW/m² insolation to collect 7.2 × 10⁶ J? Give answer in minutes.
Given: E = 7,200,000 J, I = 1000 W/m², A = 4 m²
Rearrange: t = E / (I × A) = 7,200,000 / (1000 × 4)
t = 7,200,000 / 4,000 = 1800 s
1800 s ÷ 60 = 30 minutes
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India lies in the tropical and subtropical belt, receiving 4–7 kWh/m²/day of solar energy — among the highest in the world. This is why India's solar energy capacity has grown to over 80 GW, with a target of 500 GW by 2030.