Answer :
Answer: 1.13 · 10⁸ m²; No
Explanation:
The formula for the capacitance of a parallel-plate capacitor is given as:
C = ε₀A/d, where:
- C is the capacitance (F)
- ε₀ is the vacuum permittivity (8.85 · 10⁻¹² F/m)
- A is the surface area of each plate (m²)
- d is the separation between the plates (m)
We are given:
- C = 1 F
- d = 1 mm = 0.001 m
Let's plug our known values into the formula to solve for A:
1 = (8.85 · 10⁻¹²)A/0.001
0.001 = (8.85 · 10⁻¹²)A
A = 1.13 · 10⁸ m²
This is not a realistic size for a capacitor as 1.13 · 10⁸ m² is an extremely large area. It is about the size of a city.
The capacitor requires an area of 1.13 x 10⁸ m² per plate, which is unrealistic.
To design a parallel-plate capacitor having a capacitance of 1.00 F and a plate separation of 1.00 mm required surface area of each plate can be calculated using the formula for the capacitance of a parallel-plate capacitor:
C = (ε₀ * A) / d,
Rearranging this formula to solve for the area A gives as:
A = (C * d) / ε₀
Substituting the known values:
A = (1.00 F * 1.00 x 10⁻³ m) / (8.85 x 10⁻¹² F/m) = 1.13 x 10⁸ m²
This surface area is extremely large, approximately 113 square kilometers, which is not realistic for a practical capacitor design.
