AQA A-Level Physics: Interpretation of the Area Under a Graph of Charge Against Potential Difference — mark scheme explained

The question

A capacitor with a capacitance of 3 μF is charged to a potential difference of 6 V. Calculate the energy stored in the capacitor. [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: C = 3 μF, V = 6 V

• S2

  Use the equation E = 1/2 CV 2

• S3

  Substitute the values into the equation: E = 1/2 × 3 × 10 -6 F × (6 V) 2

• S4

  Calculate the energy: E = 1/2 × 3 × 10 -6 × 36

• S5

  E = 54 × 10 -6 J = 54 μJ

Model answer

Worked through, with each step tagged to the mark it earns.

1. S1

   Identify the given values: C = 3 μF, V = 6 V

2. S2

   Use the equation E = 1/2 CV 2

3. S3

   Substitute the values into the equation: E = 1/2 × 3 × 10 -6 F × (6 V) 2

4. S4

   Calculate the energy: E = 1/2 × 3 × 10 -6 × 36

5. S5

   E = 54 × 10 -6 J = 54 μJ

6. Final answer: 54 μJ

Common mistakes

• Forgetting to use the factor of 1/2 in the energy equations. — Always include the factor of 1/2 when using the energy equations E = 1/2 QV, E = 1/2 CV 2 , or E = Q 2 /2C.
• Confusing charge (Q) with capacitance (C). — Double-check that you are using the correct symbol for each quantity. Charge is Q, and capacitance is C.
• Using the wrong units when substituting values into equations. — Ensure that all units are consistent before substituting values into equations. Convert all units to the same base unit if necessary.
• Misinterpreting the area under a graph of charge against potential difference. — Remember that the area under a linear graph of charge against potential difference is given by 1/2 × base × height, which corresponds to E = 1/2 QV.
• Failing to rearrange equations correctly when solving for unknowns. — Practice rearranging equations step-by-step. For example, to solve for C in E = 1/2 CV 2 , first isolate CV 2 and then divide by V 2 .
• Using the wrong form of the energy equation for a given problem. — Identify which quantities are given in the problem and choose the appropriate form of the energy equation. For example, if you know C and V, use E = 1/2 CV 2 .

Where the marks go

• Full worked solution (all marking points)4 marks

Related questions

• AQA A-Level Physics: Fundamental and Derived Units in Physics — mark scheme explained →
• AQA A-Level Physics: Errors and Uncertainties in Measurements — mark scheme explained →