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There are a couple of different answers to this question, depending upon just what you're looking for.

In the "usual" case, the strength of the electric field doesn't affect resistance significantly. In a conductor like carbon, for example, the strength of the applied field and the current vary linearly with one another which is equivalent to saying that the resistance is constant. This is the case for lots of materials, which is why "Ohm's Law" is called a "law."

Sometimes, however, increasing the strength of the electric field can cause something to happen that makes the resistance change suddenly. An example is when there's a lightning bolt: the resistance of the air stays relatively constant until the electric field gets so strong that the gasses ionize. Once that happens, the resistance drops suddenly and you get lightning.

Some clever physical arrangements of materials will exhibit different resistances depending upon the strength of the field (more convenient to talk about voltage here). A simple semiconductor diode, for example, has a relatively low resistance if the applied voltage has one polarity (the field is applied one way) but a high resistance if the polarity is reversed (the applied field is oriented the other way). Even in the "forward biased" direction, the resistance will be high when a low voltage (extremely weak field) is applied but will drop suddenly when the voltage passes a certain threshold. Devices like a diode exhibit nonlinear behavior, which is another way of saying their resistance varies with the voltage applied.

People can get really clever and design circuits where an electric field different from the one causing current to flow controls the resistance. These voltage-controlled resistors are typically made from FETs.

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