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Over the time interval after a difference in potential is applied between the ends of a wire, what would happen to the drift velocity of the electrons in a wire and to the current in the wire if the electrons could move freely without resistance through the wire?

Over the time interval after a difference in potential is applied between the ends of a wire, what would happen to the drift velocity of the electrons in a wire and to the current in the wire if the electrons could move freely without resistance through the wire?

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**Question:** Over the time interval after a difference in potential is applied between the ends of a wire, what would happen to the drift velocity of the electrons in a wire and to the current in the wire if the electrons could move freely without resistance through the wire? **Explanation:** This question examines the behavior of electrons and current in an ideal scenario where there is no resistance in a conductive wire. In practical scenarios, resistance causes electrons to collide with atoms, affecting drift velocity and current. However, theoretically, if electrons could move without resistance: 1. **Drift Velocity:** The drift velocity would increase continuously. Without resistance, electrons would accelerate continuously under the influence of the electric field, leading to an ever-increasing drift velocity. 2. **Current:** The current in the wire would also increase as a result. Current (I) is directly proportional to drift velocity (v_d), given by the formula I = nAe*v_d, where n is the charge carrier density, A is the cross-sectional area, and e is the elementary charge. Thus, as drift velocity increases without resistance, so does the current. This analysis provides a theoretical understanding of current flow in an ideal, resistance-free environment.
Transcribed Image Text:**Question:** Over the time interval after a difference in potential is applied between the ends of a wire, what would happen to the drift velocity of the electrons in a wire and to the current in the wire if the electrons could move freely without resistance through the wire? **Explanation:** This question examines the behavior of electrons and current in an ideal scenario where there is no resistance in a conductive wire. In practical scenarios, resistance causes electrons to collide with atoms, affecting drift velocity and current. However, theoretically, if electrons could move without resistance: 1. **Drift Velocity:** The drift velocity would increase continuously. Without resistance, electrons would accelerate continuously under the influence of the electric field, leading to an ever-increasing drift velocity. 2. **Current:** The current in the wire would also increase as a result. Current (I) is directly proportional to drift velocity (v_d), given by the formula I = nAe*v_d, where n is the charge carrier density, A is the cross-sectional area, and e is the elementary charge. Thus, as drift velocity increases without resistance, so does the current. This analysis provides a theoretical understanding of current flow in an ideal, resistance-free environment.
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