A-Level · Physics · AQA · Mark scheme decoded
AQA A-Level Physics: Dielectric Action in Capacitors and Relative Permittivity — mark scheme explained
The short answer
In this section, we will explore the dielectric action in capacitors and how it affects capacitance. We will also delve into the concept of relative permittivity and investigate the relationship between capacitance and the dimensions of a parallel-plate capacitor.
The question
A parallel-plate capacitor has plates with an area of 0.02 m 2 and a separation distance of 1 mm. The relative permittivity of the dielectric is 3. Calculate the capacitance. [Paraphrased for study — not reproduced from any exam paper.]
Mark scheme, decoded
What each mark is really for — in plain English — and the wording trap that loses it.
- S1
Identify the given values: A = 0.02 m 2 , d = 1 mm = 0.001 m, ε r = 3, and ε 0 = 8.85 × 10 -12 F/m.
- S2
Use the formula for capacitance: C = ε 0 × ε r × (A / d).
- S3
Substitute the values into the formula: C = 8.85 × 10 -12 × 3 × (0.02 / 0.001).
- S4
Calculate the result: C = 8.85 × 10 -12 × 3 × 20 = 531 × 10 -12 F = 5.31 × 10 -10 F.
- S5
The capacitance is 531 pF (5.31 × 10 -10 F).
Model answer
Worked through, with each step tagged to the mark it earns.
- S1
Identify the given values: A = 0.02 m 2 , d = 1 mm = 0.001 m, ε r = 3, and ε 0 = 8.85 × 10 -12 F/m.
- S2
Use the formula for capacitance: C = ε 0 × ε r × (A / d).
- S3
Substitute the values into the formula: C = 8.85 × 10 -12 × 3 × (0.02 / 0.001).
- S4
Calculate the result: C = 8.85 × 10 -12 × 3 × 20 = 531 × 10 -12 F = 5.31 × 10 -10 F.
- S5
The capacitance is 531 pF (5.31 × 10 -10 F).
Final answer: C = 531 pF (or 5.31 × 10 -10 F)
Common mistakes
- Forgetting to convert units (e.g., mm to m) before using the formula for capacitance. — Always check and convert units to the same system (SI units) before substituting values into formulas.
- Using the wrong formula for relative permittivity. — Memorize and understand both formulas: C = ε 0 × ε r × (A / d) and ε r = C / (C 0 ).
- Forgetting to include the permittivity of free space (ε 0 ) in calculations. — Always include ε 0 = 8.85 × 10 -12 F/m in the formula for capacitance.
- Misinterpreting the effect of dielectric on electric field and capacitance. — Understand that a dielectric reduces the electric field within the capacitor, thereby increasing its capacitance.
- Confusing relative permittivity (ε r ) with absolute permittivity (ε). — Remember that ε r is a dimensionless quantity, while ε = ε 0 × ε r has units of F/m.
- Forgetting to align polar molecules in the presence of an electric field. — Understand that polar molecules align along the direction of the electric field, reducing the overall electric field within the dielectric material.
Where the marks go
- Full worked solution (all marking points)4 marks