OCR A Physics · Module 4: Electrons, waves and photons
Charge & current: practice questions with answers
6 exam-style questions on charge & current. Try each one on paper first, then open the answer to see the full working and the common slips that cost marks.
- Unit prefixes2 marks
A current of 3.2 mA flows through a wire for 5.0 s. Calculate the number of electrons passing a point in the wire in this time.
N = electrons
Show the answer and working
Answer N = 1.00 × 10¹⁷ electrons
Q = It = 3.2 × 10⁻³ × 5.0 = 1.6 × 10⁻² C. N = Q ÷ e = 1.00 × 10¹⁷.
- Got 1.00 × 10²⁰ electrons? You used 3.2 A instead of 3.2 mA. I = 3.2 × 10⁻³ A, so N = It ÷ e = 1.00 × 10¹⁷.
- Got 1.00 × 10¹⁴ electrons? You converted mA to A using 10⁻⁶. 1 mA = 10⁻³ A, so N = (3.2 × 10⁻³ × 5.0) ÷ 1.6 × 10⁻¹⁹ = 1.00 × 10¹⁷.
- Using the right equation3 marks
A copper wire of diameter 1.8 mm carries a current of 4.5 A. The number density of free electrons in copper is 8.5 × 10²⁸ m⁻³. Calculate the mean drift speed, in mm s⁻¹.
v = mm s⁻¹
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Answer v = 0.13 mm s⁻¹
A = π(0.90 × 10⁻³)² = 2.54 × 10⁻⁶ m². I = nAve gives v = 4.5 ÷ (8.5 × 10²⁸ × 2.54 × 10⁻⁶ × 1.6 × 10⁻¹⁹) = 0.13 mm s⁻¹.
- Got 0.0325 mm s⁻¹? You used the diameter as the radius. A = π(0.90 × 10⁻³)² = 2.54 × 10⁻⁶ m², so v = I ÷ nAe = 0.13 mm s⁻¹.
- Got 0.102 mm s⁻¹? You used d² for the area. A = πd²/4 = 2.54 × 10⁻⁶ m², so v = I ÷ nAe = 0.13 mm s⁻¹.
- Unit prefixes1 mark
A lamp carries a current of 0.30 A for 12 minutes. Calculate the charge that flows through it.
Q = C
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Answer Q = 216 C
Time = 12 × 60 = 720 s. Q = It = 0.30 × 720 = 216 C.
- Got 3.6 C? You used 12 minutes as 12 s. Convert to seconds: 12 × 60 = 720 s, so Q = It = 0.30 × 720 = 216 C.
- Got 4.17 × 10⁻⁴ C? You divided instead of multiplying. Q = It = 0.30 × 720 = 216 C.
- Unit prefixes2 marks
A charge of 15 mC passes through a resistor and transfers 0.12 J of electrical energy to thermal energy. Calculate the potential difference across the resistor.
V = V
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Answer V = 8 V
V = W ÷ Q = 0.12 ÷ (15 × 10⁻³) = 8 V.
- Got 0.008 V? You used 15 mC as 15 C. Q = 15 × 10⁻³ C, so V = W ÷ Q = 0.12 ÷ 0.015 = 8 V.
- Got 1.8 V? You multiplied energy by charge. V = W ÷ Q = 0.12 ÷ 0.015 = 8 V.
- Using the right equation1 mark
In a metal wire, in which direction do the charge carriers move relative to conventional current?
- A In the same direction as conventional current.
- B In the opposite direction to conventional current.
- C Randomly, with no net movement.
Show the answer and working
Answer B: In the opposite direction to conventional current.
Electrons are negative, so they drift opposite to conventional current.
- Why not A? Conventional current is defined as the flow of positive charge; electrons are negative and move the other way.
- Why not C? Electrons drift in one direction when a p.d. is applied, even though they also move randomly.
- Using the right equation1 mark
Two wires are made of the same metal and carry the same current. Wire B has half the diameter of wire A. How does the drift speed in B compare with A?
- A It is twice as large.
- B It is the same.
- C It is four times as large.
Show the answer and working
Answer C: It is four times as large.
v = I ÷ nAe and A ∝ d², so halving d quarters A and multiplies v by four.
- Why not A? The area depends on diameter squared, so halving the diameter quarters the area and the speed is four times larger.
- Why not B? The speed is not the same: I = nAve means v is inversely proportional to the area.