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If I have a voltage difference V from terminal 1 to terminal 2 of a resistor. I take an arbitrary point P along the resistor, between terminal 1 and terminal 2, and take terminal 1 as a voltage reference. Does the voltage difference between the point P and terminal 1 increases from 0 at terminal 1 to V at terminal 2 ? Is there a voltage gradient across a resistor ?

The question is about circuit theory in general.

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  • \$\begingroup\$ for metal film, yes there will be a voltage gradient along a resistor. You can see this, using the tip of a scope probe, with the scope-calibration voltage passing thru the resistor. \$\endgroup\$ – analogsystemsrf Sep 1 '19 at 22:45
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An ideal resistor is indivisible, so you can't really talk about voltages inside the resistor.

A real resistor comprises some kind of resistive material: a carbon slug, a long wire, a thin metal or carbon film, for example. If you could trace a path from one terminal of the resistor, across this resistive material, to the other terminal of the resistor then you would indeed see a voltage gradient.

Having said that, you shouldn't assume that there is a linear gradient as you move across any physical dimension of the resistor.

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Yes. Resistors are made in many different ways but consider a wire wound resistor. As you move from your reference terminal 1 to terminal 2 you increase resistance and potential difference.

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