The questions are on the capacitors test. Take it under real conditions before reading the mark scheme.
Quick answer: A capacitor stores charge on two plates separated by an insulator, with capacitance C = Q/V in farads. This mark scheme gives the model answers and the marks for the 8 questions of the AP Physics 2 test on capacitors, from capacitance to doubling the voltage, with the equivalent answers to accept.
Award marks as shown for the relation, the substitution and the final answer with unit. For explanations, accept any clear statement of the physical idea. Do not penalise the same unit mistake more than once.
Level: AP Physics 2 (algebra-based) · Curriculum: AP P2 Unit 10
Question 1 Capacitance (2 marks)
(a) Capacitance is the charge stored per unit voltage, C = Q/V.
(b) C = 12 / 3.0 = 4.0 μF.
Marking: 1 mark for each part.
Question 2 Parallel plates (3 marks)
(a) C = ε₀A/d = (8.85 × 10⁻¹²)(0.030) / (5.0 × 10⁻⁴) = 5.3 × 10⁻¹⁰ F (531 pF).
(b) C is inversely proportional to d, so it halves.
Marking: (a) 1 mark for the substitution, 1 mark for the answer; (b) 1 mark.
Question 3 Energy in a flash unit (3 marks)
Q = CV = 220 × 10⁻⁶ × 24 = 5.3 × 10⁻³ C. U = ½CV² = 0.5 × 220 × 10⁻⁶ × 24² = 6.3 × 10⁻² J (63 mJ).
Marking: 1 mark for Q; 1 mark for the energy relation; 1 mark for the energy value.
Question 4 Battery stays connected (3 marks)
New C = 3.0 × 2.0 = 6.0 μF. Before: Q = 2.0 × 12 = 24 μC. After: Q = 6.0 × 12 = 72 μC.
Marking: 1 mark for the new C; 1 mark for stating that the voltage is fixed; 1 mark for the two charges.
Question 5 Isolated capacitor (3 marks)
The charge stays the same; C increases; V decreases (V = Q/C); and U = Q²/2C decreases. The lost energy is work done by the capacitor in pulling the dielectric in. Q constant, V and U fall.
Marking: 1 mark for Q constant and C up; 1 mark for V and U down; 1 mark for the explanation.
Question 6 Voltage against charge (2 marks)
The gradient is 1/C. The shaded area is the energy stored, ½QV.
Marking: 1 mark for each.
Question 7 Breakdown (2 marks)
The field between the plates is E = V/d. If the field is too large, the insulator ionises and starts to conduct, causing a spark and damage. The rating keeps E below this limit.
Marking: 1 mark for E = V/d rising with V; 1 mark for breakdown of the dielectric.
Question 8 Doubling the voltage (2 marks)
The capacitance stays the same because it depends only on geometry and the dielectric. The energy is ½CV², so it becomes four times larger.
Marking: 1 mark for each.
