After the teflon slab is inserted between the plates, the gap between the plates of the capacitor will decrease, which will lead to an increase in its capacitance. The capacitance of the capacitor can be determined by the formula:
C = ε₀εᵣA/d,
where C is the capacitance of the capacitor, ε₀ is the permittivity of free space, εᵣ is the relative permittivity of the material, A is the area of the capacitor plates, and d is the distance between the plates.
For an air gap with distance d₁ between the plates, the capacitance of the capacitor is:
C₁ = ε₀A/d₁ = 8.854 x 10⁻¹² x 25 x 10⁻⁶ / 0.001 = 221 pF.
After the teflon slab is inserted, the gap between the plates decreases to d₂. The relative permittivity of teflon is εᵣ = 2.1.
The new capacitance C₂ can be calculated as:
C₂ = ε₀εᵣA/d₂.
The increase in the capacitance of the capacitor after the insertion of the teflon slab can be calculated by the ratio:
ΔC/C₁ = (C₂ - C₁)/C₁ = (εᵣ - 1) x (d₁/d₂ - 1).
The ratio d₁/d₂ is determined by the ratio of the areas of the teflon slab and the capacitor plates.
Assuming that the thickness of the teflon slab is much smaller than the dimensions of the capacitor plates, we can assume that the area of the teflon slab is equal to the area of the capacitor plates. Then:
d₁/d₂ = (A - S)/A,
where S is the area of the teflon slab.
If the area of the teflon slab is 10% of the area of the capacitor plates, then:
S = 0.1 x A = 0.1 x 25 x 10⁻⁶ = 2.5 x 10⁻⁶ m².
Then:
d₁/d₂ = (A - S)/A = (25 x 10⁻⁶ - 2.5 x 10⁻⁶) / 25 x 10⁻⁶ = 0.9.
Substituting the values into the formula for the increase in capacitance, we get:
ΔC/C₁ = (εᵣ - 1) x (d₁/d₂ - 1) = (2.1 - 1) x (0.9 - 1) = -0.09.
Therefore, the capacitance of the capacitor after the insertion of the teflon slab will be:
C₂ = C₁ x (1 + ΔC/C₁) = 221 x (1 - 0.09) = 202 pF.
Thus, after the insertion of the teflon slab, the capacitance of the capacitor will increase from 25 pF to 202 pF.