Question

1. At the radius of the earth's orbit, the intensity of sunlight is I = 1.4 kW.m^-2 . (This means that 1.4 kW.m^-2 passes through 1 square metre at right angles to the sun's rays.) The solar array in the previous question consists of 10 panels, each with area A = 1.6 m^2 . Under optimal conditions - with the sun at right angles to the array and no clouds in the sky - the array produces P out = 2.3 kW .


What is the efficiency of the array? Power out/power in = _____ %.


2. Here is an extract from our electricity bill. The colored text has been added to highlight the rate, with the 'rate' being the price per kW.hr:


We buy energy at:


Used energy x rate = cost

92 days ( 294.3 kWh) 24.9000 c 73.27 dollars


Energy Purchased x rate = credit

92 days ( 883.4 kWh) 6.6000 c 58.30 dollars

Answer 1

1. What the solar array receives from the sun:

$$P_{in}=NAI=10\cdot1.6\cdot1.4=22.4\text{ kW}.$$

Efficiency:

$$\eta=\frac{P_{out}}{P_{in}}\cdot100\%=\frac{2.3}{22.4}\cdot100\%=10.3\%.$$

Interestingly, the most efficient and modern solar panels can convert only 23% of the solar energy to electrical energy.