AQA A-Level Physics Paper 1, June 2022: Question 30

✅ Correct Answer: D (25 Ω)

Option D cannot be made using three 10 Ω resistors. Let's look at why the other options can be made:

• A (3.3 Ω): Three resistors in parallel give 1/R = 1/10 + 1/10 + 1/10 = 3/10 , so R = 10/3 = 3.33 Ω . (Possible)
• B (6.7 Ω): Two resistors in parallel ( 5 Ω ) combined in series with a third resistor ( 10 Ω ) gives 5 + 1.67... wait, let's check: two in parallel ( 5 Ω ) + one in series = 15 Ω ? No! Two in parallel give 5 Ω , in series with one 10 Ω gives 15 Ω ? Let's re-verify combinations: Two in series ( 20 Ω ) in parallel with one 10 Ω gives (20 × 10) / (20 + 10) = 200 / 30 = 6.67 Ω . (Possible)
• C (15 Ω): Two resistors in parallel ( 5 Ω ) in series with one resistor ( 10 Ω ) gives 5 + 10 = 15 Ω . (Possible)

💡 Key Knowledge

• Series formula: R_total = R₁ + R₂ + R₃ (increases total resistance).
• Parallel formula: 1 / R_total = 1 / R₁ + 1 / R₂ + 1 / R₃ (decreases total resistance).
• Mixed combinations: You can also put two resistors in series/parallel and the third in the opposite configuration. Total possible distinct resistance values for three identical resistors is 4.

🧠 Exam Technique

In multiple-choice questions where you need to find what cannot be made, work through the options systematically or calculate the absolute minimum and maximum bounds first:

• Maximum resistance: All three in series = 10 + 10 + 10 = 30 Ω .
• Minimum resistance: All three in parallel = 10 / 3 = 3.3 Ω .
• Since 25 Ω is well within the 3.3 Ω to 30 Ω range, you must test the mixed topologies to see if 25 Ω is mathematically constructible. Trying to make 25 Ω requires branches that do not integer-match with 10 Ω components.

❌ Common Errors

• Guessing blindly without writing down the parallel/series combination rules.
• Confusing the formulas for resistors and capacitors (remember: resistors in series add directly, whereas capacitors in series use reciprocal addition).