Final answer:
To find the capacitance of a plane capacitor, one calculates by using the formula C = εᵣ · A/d, after converting the given dimensions to standard SI units. The calculated capacitance for the provided parameters is 4.425 × 10-14 farads (F).
Step-by-step explanation:
To determine the capacitance of a plane capacitor with an area of 10 cm² per plate, separated by 1 cm, and filled with a dielectric material having εᵣ = 5ε₀, we use the formula for capacitance of a parallel-plate capacitor filled with a dielectric material:
C = εᵣ · A/d
Where:
- C is the capacitance
- εᵣ is the permittivity of the dielectric material
- ε₀ is the permittivity of free space, 8.85 × 10-12 F/m
- A is the area of one plate in square meters (m²)
- d is the separation between the plates in meters (m)
First, we convert the area from cm² to m²:
A = 10 cm² = 10 × 10-4 m²
Next, we convert the distance from cm to m:
d = 1 cm = 0.01 m
Now we can calculate the capacitance:
C = 5 × 8.85 × 10-12 F/m × (10 × 10-4 m²) / 0.01 m
C = 4.425 × 10-12 F/m × 1 × 10-2 m² / 0.01 m
C = 4.425 × 10-14 F
Therefore, the capacitance of the plane capacitor is 4.425 × 10-14 farads (F).