Potential drop inside a circuit as a E=gradV

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Discussion Overview

The discussion revolves around the concept of potential drop in a circuit, particularly in relation to the electric field and the equation E=grad(V). Participants explore whether a potential drop occurs along a wire in a circuit, independent of resistance, and how electric fields influence voltage measurements in conductors.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions why potential does not drop along a wire in a circuit if an electric field exists, suggesting that the drop should occur regardless of resistance.
  • Another participant agrees that real wires have finite resistance, leading to a voltage drop, but notes that this drop is often negligible compared to the rest of the circuit.
  • A different participant emphasizes that the potential drop is related to electric fields rather than resistance, arguing that voltage should decrease gradually along the wire due to the electric field present.
  • In response, a participant explains that conductors allow charges to move in response to the electric field, which can lead to a situation where the voltage measured across a wire remains approximately constant due to the accumulation of charges setting up their own electric field.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between electric fields, potential drops, and resistance in wires. There is no consensus on whether a potential drop occurs along the wire independent of resistance, and the discussion remains unresolved.

Contextual Notes

The discussion highlights assumptions about the behavior of electric fields in conductors and the role of resistance, but does not resolve the implications of these factors on potential measurements.

Joker93
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Considering that the electric field exist outside a battery in a wire,shouldnt the potential drop while we move along the wire even if there is no resistor(E=grad(V))?Because when i see diagrams of potential along the wire,they all show a constant potential along the wire until it reaches a resistor in which the potential drops.
 
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You are correct. A real wire has finite resistance and you will lose voltage as you go along the wire. Usually the voltage drop in the wire is so much less than the rest of the circuit that it can be ignored, but not always.
 
@Drakkith i am talking about something else.forget the resistance of the wire.We know from electrostatics that voltage drops gradually when there is an electric field.So,why does the potential not drop inside the circuit when we move along the wire?it has nothing to do with resistance but everything to do with electric fields
 
Last edited:
Because a conductor is composed of charges that can move in response to the electric field. If you attach a long wire with a small capacitance to each plate of a capacitor, the charges in the wires move in response to this electric field. Measuring the voltage between the ends of these wires will give you approximately the same voltage as there is between the two plates because the charges have moved in response to the field and accumulated, setting up their own electric field that gives you a voltage between the ends of the wires.
 

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