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We know that the resistance increase with temperature or for exemple in an AC circuit, the resistance is superior to the same resistor for DC current due to skin effect. But my question is for a same resistor having variable resistance, does the electric field inside this resistor change? let's take for example in DC circuit having 2 resistors and 1 EMF : first one R1 variable with temperature and second one R2 constant. we know that the voltage across R1 is equal to U = R1 * EMF/(R1+R2). let's say for exemple R1 change due to change of temperature, thus U will change and we know that U =integral of E.dl thus E will decrease right? But we know that the resistance of the resistor will increase so the electron will have more "difficulties" to flow inside the resistor but how this will decrease the electric field?

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  • $\begingroup$ Are these two resistors in series? If the resistance goes up, so will the electric field (as the resistor experiences a greater fraction of the total potential difference). $\endgroup$ – Floris Dec 26 '14 at 1:01
  • $\begingroup$ We have plenty of materials that have a negative temperature coefficient of resistance. You can find over 4000 NTC components at mouser.com. EMF is a matter of the voltage source, not the resistors in the circuit. It's not clear to me what you are asking. $\endgroup$ – CuriousOne Dec 26 '14 at 1:01
  • $\begingroup$ Yes Floris in Series, sorry the electric field will increase so we can say the "electric system" will adapt to the change of the resistor right? $\endgroup$ – tonyjk Dec 26 '14 at 1:03
  • $\begingroup$ CuriousOne im talking in general about variable resistors, if it changes we know that the flow of electrons will be affected but as we know U = integral of E.dl so how this will affect the electric field inside it $\endgroup$ – tonyjk Dec 26 '14 at 1:06
  • $\begingroup$ The electric field is not affected by the resistance. You are simply using a circuit that doesn't leave the electric potential constant. That's property of the circuit, not of the resistor. $\endgroup$ – CuriousOne Dec 26 '14 at 1:24
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The electric field in a component is just a function of the voltage across it, and the composition of the component. So for a uniform resistor (regardless of the temperature coefficient), the electric field is $E = V/\ell$ where $\ell$ is the distance between the electrodes.

Therefore, if you have two resistors in series, with resistance $R_1$ and $R_2$, as you say the voltage will be divided among them in accordance with their resistance - and if the resistance of one of them increases (for example because of heating), it will get a larger share of the voltage and thus the electric field will be larger inside this resistor.

The electric field drives the electrons - the more resistance they encounter, the larger the field they need in order to allow for a certain current.

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