AQA AS Level Physics Paper 2, June 2023: Question 29

Calculating Number of Charge Carriers in a Resistor

AQA AS Level Physics • Multiple Choice Question

What this question tests

This question assesses your understanding of electric current as the rate of flow of charge, your ability to convert standard prefixes (milliamps) and units of time (minutes to seconds), and your knowledge of elementary charge to find the total number of individual electrons passing a point.

Question 29: Current and Charge Calculation

Determining the total number of electrons in a given time

✅ Correct Answer

Option B: 1.7 × 10¹⁹

Mark Awarded: 1 / 1 for selecting B.

💡 Key Knowledge

Definition of current: I = Q / t , rearranged as Q = I × t .
Quantisation of charge: Q = N × e , where N is the number of electrons and e is the elementary charge ( 1.60 × 10⁻¹⁹ C found on your data booklet).
Unit conversions: 1 mA = 10⁻³ A and 1 minute = 60 seconds .

🧠 Exam Technique

Always convert all values into SI base units (Amperes and Seconds) before running your calculations. Doing this straight away prevents catastrophic powers-of-ten errors.

❌ Common Errors

Forgetting time conversion: Multiplying current by 3 directly instead of converting 3 minutes to seconds ( 3 × 60 = 180 s ).
Mishandling prefixes: Forgetting to multiply 15 mA by 10⁻³ .
Inverse division: Dividing elementary charge by total charge instead of total charge by elementary charge ( Q / e ).

📐 Step-by-Step Calculation

Convert current to amperes:
I = 15 mA = 15 × 10⁻³ A
Convert time to seconds:
t = 3 minutes = 3 × 60 = 180 s
Calculate total charge (Q):
Q = I × t = (15 × 10⁻³ A) × (180 s) = 2.7 C
Find the number of electrons (N):
N = Q / e = 2.7 C / (1.60 × 10⁻¹⁹ C) = 1.6875 × 10¹⁹ ≈ 1.7 × 10¹⁹