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In free space, a potential difference is required for the flow of a charge though there is no resistance. In a conductor, a potential difference is required only to overcome the resistance, am I right? If yes, then is this an assumption of Ohm's law that “potential difference is required only to overcome the resistance”?

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In free space, a potential difference is required for the flow of a charge though there is no resistance.

Not true. Launch an electron into space and it will continue to move due to inertia, even if the electric field is 0.

In a conductor, a potential difference is required only to overcome the resistance, am I right?

I don't know what's "required", but if you apply a potential difference across a conductor then current will flow, and if you apply 0 potential difference across the conductor no current will flow.

then is this an assumption of Ohm's law that “potential difference is required only to overcome the resistance”?

Ohm's law is an observation that the current through a conductor is proportional to the applied potential difference. That potential difference is required for current flow in a conductor is a consequence of Ohm's Law, not an assumption used to develop the "law".

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Ohms law relates the potential needed to maintain a constant current under the influence of some resistive force

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The potential difference between two points is the difference in potential energy that an electron will have if it travels from one to the other. An electron that travels from the - terminal to the + terminal of a 3 Volt battery will lose 3 electron Volts (aka 3 eV).

Potential energy is associated with a force. For example, you lose gravitational potential energy if you move from a high position to a low one, moving in the direction of the force of gravity.

In a circuit, the battery generates an electric field. The field generates a force that pushes electrons around the circuit. In order to travel around the circuit, an electron must overcome all forces that push back, and may be helped by forces in the direction of the flow.

This oversimplifies things of course.

First, no individual electron moves all the way around a circuit in any short time. Instead, one electron pushes on the next. The battery pushes an electron into one end, and a different electron pops out the other end.

The force that impede the flow in Ohm's law are complex. It takes quantum mechanics to describe them. And they are not completely understood.

Circuits may contain capacitors and inductors. A flowing current makes charge accumulate on the plates of a capacitor. The charge creates a repulsion that impedes the flow of more electrons.

A current in an inductor generates a magnetic fields that store energy. The energy must come from the electrons flowing through the circuit. As the field builds, a back voltage is generated, a force impeding the flow. On the other hand, if the current is reduced, the magnetic field generates a voltage, a force, that propels the electrons forward and keeps the current flowing. An inductor resists changes to current.

Diodes, transistors, and similar components also impede or permit a current flow. Again, how they work is best described quantum mechanically.

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In free space, a potential difference is required for the flow of a charge though there is no resistance.

No. A potential difference $V$ between two points is the work required per unit charge to move the charge between the two points. If there is no resistance, no work is required to move charge. The charge can move through the space at constant velocity. A mechanical analogy is no work would be required for an object to slide with constant velocity on a frictionless surface.

However, if a voltage (potential difference) is applied across the free space and free electrons are available (e.g., electrons generated at the cathode of a cathode ray tube) then the force applied by the electric field will accelerate the electrons across the space. The kinetic energy acquired by the charge is then the work per unit charge done by the voltage source.

In a conductor, a potential difference is required only to overcome the resistance, am I right?

If you wish to move charge through electrical resistance, then a voltage (potential difference) must be applied to accomplish that. But a potential difference can exist between two points without any charge moving between the two points. An example is a fully charged capacitor in a dc circuit.

If yes, then is this an assumption of Ohm's law that “potential difference is required only to overcome the resistance”?

The law was not based on the assumption that a potential difference is required to overcome resistance. It was based on the observation that a linear linear relationship exists between the potential difference (voltage) across a resistor and the current flowing through the resistor, with the slope being the resistance.

Hope this helps.

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