18. Two identical wires X and Y are connected with a switch to a cell of negligible internal

Two identical wires X and Y are connected with a switch to a cell of negligible internal resistance as shown. The electrons in wire Y have a drift speed v when the switch is open. The switch is closed. What is the drift speed of electrons in wire X?
A. v
B. v/2
C. 2v
D. 4v
Correct Answer: A
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Corrected Overview of the Problem
This MCQ from IBDP Physics SL Paper-1, May 2023, challenges you to predict the change in drift speed when two identical wires are connected in parallel to a battery with negligible internal resistance.
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When the switch is open, only wire Y is in the circuit, so the current through it is given by I=V/R, where V is the battery voltage and R is the resistance of wire Y. The drift speed of electrons in wire Y at this point is v.
When the switch is closed, both wires X and Y are connected in parallel. The total resistance of the circuit now becomes R/2, so the total current from the battery doubles to 2I. However, since the wires are identical, this total current splits equally, with each wire carrying the original current III.
Therefore, the drift speed of electrons in wire X (and Y) remains the same as when only one wire was connected. This means that even though the total current in the circuit changes, the current through each identical wire remains III, keeping the drift speed at v.
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Enrichment: Key Concepts in This Problem
• Parallel Circuits and Current Splitting: In a parallel circuit with identical resistances, the total current splits equally among the branches. This principle applies directly here since wires X and Y have the same resistance.
• Drift Speed and Current: Drift speed is directly proportional to the current flowing through a conductor. However, since the current through each identical wire remains the same as before (even though the total circuit current changes), the drift speed also remains unchanged.
• Impact of Resistance on Current: When identical wires are connected in parallel, the effective resistance of the circuit decreases. This leads to an increase in total current from the battery but does not affect the individual branch currents when wires are identical.
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Relevance to IBDP Curriculum
This problem fosters several learner profiles and skills:
• Thinkers: Encourages logical reasoning to connect multiple concepts like current division and resistance.
• Inquirers: Sparks curiosity about how circuits behave when components are rearranged.
• Knowledgeable: Reinforces understanding of current, resistance, and drift speed in electrical circuits.
Skills developed include:
• Conceptual reasoning: Applying principles of parallel circuits to understand drift speed behavior.
• Problem-solving: Encourages analytical thinking to predict outcomes without relying on equations.
• Transferable knowledge: Enhances understanding of parallel circuits, useful for real-world applications in electrical systems.
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Suggested Enquiry Questions for Further Discussion
1. If the resistance of wire X were doubled, how would the current and drift speed in each wire change?
2. How does the behavior of drift speed change if the wires have different cross-sectional areas?
3. What would happen to the total current and drift speed if three identical wires were connected in parallel?
4. Why does the total resistance decrease when resistors are connected in parallel?
5. Can the same logic apply to other components like capacitors in parallel circuits?
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Instruction to Students
Pause the video here and try solving the problem on your own. Consider what happens to the current in parallel circuits and how it impacts the drift speed. If you're stuck, continue watching the video for the explanation and solution.
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