Supercapacitors, with capacitance of 1.00F or more, are made with plates that have a spongelike structure with a very large surface area. Determine the surface area of a supercapacitor that has capacitance of 1.0F and an effective separation between the plates of d=1.0 mm
So this is what I did,
A=dc/epsilon= [1.0E-3 m (1.00F)]/8.85e-12 F/m
= 1.13e8 m^2
The answer in the back of the book is 1.0e2 km^2
If I round my answer it will be 1.0e5 km^2, so I don't know why they got that... am I using the correct formula?
Yes, you are using the correct formula to calculate the surface area of the supercapacitor. The formula you used, A = dc/ε, is correct. Here's a breakdown of the calculation:
Given:
Capacitance (C) = 1.0 F
Plate separation (d) = 1.0 mm = 1.0 × 10^(-3) m
Now, substituting these values into the formula:
A = (1.0 × 10^(-3) m) × (1.0 F) / (8.85 × 10^(-12) F/m)
Calculating the denominator:
1.0 F / (8.85 × 10^(-12) F/m) = 1.13 × 10^(11) m
Multiplying this with the plate separation:
A = (1.0 × 10^(-3) m) × (1.13 × 10^(11) m)
= 1.13 × 10^(8) m^(2)
So, based on your calculations, the surface area of the supercapacitor is approximately 1.13 × 10^(8) m^(2).
However, the given answer in the book is 1.0 × 10^(2) km^(2), which is 100,000 km^(2). It seems like there might be an error in the book's answer or a mistake in the conversion.
To convert the surface area from m^(2) to km^(2), you would divide by (1000 m/km)^2, which gives:
(1.13 × 10^(8) m^(2)) / (1000 m/km)^2 ≈ 1.13 × 10^(2) km^(2).
As you can see, it is closer to the book's answer but still slightly different. It's possible that there was a rounding error or an alternate method used in the book's solution.