A parallel plate capacitor has area of 2cm^2 and a plate separation of 1mm. Find capacitance.
To find the capacitance of a parallel plate capacitor, we can use the formula:
C = (ε₀ * A) / d
Where:
- C is the capacitance
- ε₀ is the permittivity of free space (approximately 8.85 x 10^-12 F/m)
- A is the area of the plates
- d is the distance between the plates
Given:
A = 2 cm^2 = 2 x 10^-4 m^2 (since 1 cm = 0.01 m)
d = 1 mm = 0.001 m
Plugging in these values into the formula, we can calculate the capacitance:
C = (8.85 x 10^-12 F/m) * (2 x 10^-4 m^2) / (0.001 m)
C = 8.85 x 10^-12 F/m^3 / 0.001 m
C = 8.85 x 10^-12 F/m²
Therefore, the capacitance of the parallel plate capacitor is approximately 8.85 x 10^-12 F/m².
To find the capacitance of a parallel plate capacitor, you can use the formula:
C = ε₀ * (A/d)
Where:
C is the capacitance of the capacitor,
ε₀ is the vacuum permittivity (a constant value),
A is the area of the plates, and
d is the distance between the plates.
Now let's calculate the capacitance for the given values.
Given:
Area (A) = 2 cm^2 = 2 * 10^(-4) m^2 (since 1 cm = 10^(-2) m)
Plate separation (d) = 1 mm = 1 * 10^(-3) m (since 1 mm = 10^(-3) m)
First, let's calculate the vacuum permittivity (ε₀). The vacuum permittivity is a constant value equal to approximately 8.854 x 10^(-12) F/m.
Now, substitute the given values into the formula:
C = 8.854 x 10^(-12) F/m * (2 * 10^(-4) m^2 / 1 * 10^(-3) m)
Next, simplify the calculation:
C = 8.854 x 10^(-12) F/m * 2 * 10^(-4) m / 1 * 10^(-3) m
= 8.854 x 10^(-12) F * 2 / 1
= 1.7708 x 10^(-11) F
Therefore, the capacitance of the parallel plate capacitor is approximately 1.7708 x 10^(-11) F.