A solar cell that is 15% efficient in converting solar to electric energy produces an energy flow of 1.00 kW/#\text(m)^2# when exposed to full sunlight. The cell has an area of 30.0 #\text(cm)^2#. (a) What is the power output of the cell, in watts?
Two sections:
- What is the power output of the cell, in watts?
- If the power calculated in part (a) is produced at 0.45 V , how much current does the cell deliver?
Two sections:
- What is the power output of the cell, in watts?
- If the power calculated in part (a) is produced at 0.45 V , how much current does the cell deliver?
1 Answer
Here's what I got.
Explanation:
Start by calculating the energy flow of the solar cell in kilowatts per square centimeter,
#color(blue)(ul(color(black)("1 m"^2 = 10^4"cm"^2)))#
to find
#1.00 "kW"/color(Red)(cancel(color(black)("m"^2))) * (1color(Red)(cancel(color(black)("m"^2))))/(10^4"cm"^2) = 1.00 * 10^(-4) "kW cm"^(-2)#
Now, you know that the total surface of the solar cell is equal to
#30.0 color(Red)(cancel(color(black)("cm"^2))) * (1.00 * 10^(-4)"kW")/(1color(Red)(cancel(color(black)("cm"^2)))) = 3.00 * 10^(-3)"kW"#
The cell is said to have an efficiency of
In your case, this efficiency will produce a power output of
#3.00 * 10^(-3)color(Red)(cancel(color(black)("kW input"))) * "15 kW output"/(100color(Red)(cancel(color(black)("kW input")))) = 4.5 * 10^(-4)"kW"#
Finally, to convert this to watts, use the fact that
#color(blue)(ul(color(black)("1 kW" = 10^3"W")))#
You will end up with
#4.5 * 10^(-4) color(Red)(cancel(color(black)("kW"))) * "1 W"/(10^3color(Red)(cancel(color(black)("kW")))) = color(darkgreen)(ul(color(black)("0.45 W")))#
The answer is rounded to two sig figs, the number of sig figs you have for the efficiency of the solar cell.
For part (b), use the fact that
#color(blue)(ul(color(black)(P = I * V)))#
Here
#P# is electric power#I# is electric current#V# is voltage
Rearrange to solve for
#P = I * V implies I = P/V#
Keeping in mind that in terms of units you have
#color(blue)(ul(color(black)("1 W" = "1 A" * "1 V")))#
plug in your values to find
#I = (0.45color(red)(cancel(color(black)("V"))) * "A")/(0.45color(red)(cancel(color(black)("V")))) = color(darkgreen)(ul(color(black)("1.0 A")))#