Explain why two identical resistors connected in parallel have a combined resistance that is less than the resistance of either individual resistor, using a model of current flow through conducting materials.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
Model answer (4 marks)
In a conductor the current is carried by free electrons that drift through the material when an electric field (potential difference) is applied.
When two identical resistors are wired in parallel, the electrons have two independent paths to follow. The effective cross‑sectional area for electron flow is therefore increased.
Because each resistor carries its own current, the total current drawn from the source is the sum of the two currents. For the same applied voltage, the total current is larger than that through a single resistor.
Since resistance is defined by R=V/I, a larger I for the same V gives a smaller R. Thus the combined resistance of the parallel pair is less than the resistance of either resistor alone.
When two identical resistors are wired in parallel, the electrons have two independent paths to follow. The effective cross‑sectional area for electron flow is therefore increased.
Because each resistor carries its own current, the total current drawn from the source is the sum of the two currents. For the same applied voltage, the total current is larger than that through a single resistor.
Since resistance is defined by R=V/I, a larger I for the same V gives a smaller R. Thus the combined resistance of the parallel pair is less than the resistance of either resistor alone.
Examiner tips
- Use the definition R=V/I to link current and resistance
- Explain that parallel gives extra pathways, increasing effective area
- Show that total current is the sum of the two currents
- Mention that the same voltage is applied to both resistors
Common mistakes
- Confusing series and parallel arrangements
- Failing to state that the voltage across each resistor is the same
- Using the wrong formula for combined resistance (e.g., adding resistances instead of using 1/R=1/R1+1/R2)
Mark scheme (4 marks)
- In a conducting material, current is carried by free (conduction) electrons moving through the material in response to an electric field / potential difference.
- Connecting resistors in parallel provides additional pathways (cross-sectional area through which electrons can flow is effectively increased).
- For the same applied potential difference, the total current drawn from the source is greater than through a single resistor alone, because each resistor independently carries its own current.
- Since resistance R = V/I, a larger total current for the same voltage gives a smaller combined resistance, which is therefore less than either individual resistor's resistance.
Key terms in this question
Related
- All IB DP Physics Higher Level (2023 syllabus) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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