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A current 1 ampere passed through a conductor which resistance is 10 ohms, if the current become 2 amperes, then will the resistance of the conductor will remain 10 ohms, and if not, then what is the resistance in the second case?

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    – ACuriousMind
    Mar 10 '19 at 11:47
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There is not sufficient information to answer this question.

For starters, the question contradicts itself. A conductor is something with (close to) zero resistance. A conductor with a resistance of 10 ohms is not a (perfect) conductor. But let's say that 10 ohms is good enough to call something a "conductor". After all, 400 feet of 24 Gauge copper wire has a resistance of 10 ohms and we call "copper wire" a conductor.

400 feet of 24 Gauge copper wire has a resistance of 10 ohms. If you run 1 ampere of current through it then the 400 feet of 24 Gauge copper wire has a resistance of 10 ohms. If you run 2 amperes of current through it then the 400 feet of 24 Gauge copper wire still has a resistance of 10 ohms. That's because 400 feet of 24 copper wire has a resistance of 10 ohms.

Sure, if you run enough current through the wire then eventually it'll heat up and the resistance will increase, but that's not something you'll see a large effect from under ordinary operating conditions. (2 amperes is below the 3.5 ampere maximum current rating of 24 Gauge copper wire.) Figuring out how much something's resistance changes when you run current through it is a complicated process. It depends on how hot the wire gets. How hot the wire gets depends on heat dissipation. Heat dissipation depends on all sorts of things from the material it's made of to the density and temperature of the surrounding air.

Your question never specified that you're using 400 feet of 24 Gauge copper wire. It could be 12 Gauge copper wire. It could be silver wire. You could be running current through a transister, for which the meaning of the word "resistance" becomes very complicated very fast.

Fortunately, we usually use the word "resistance" to describe an electrical component called a "resistor". The great thing about resistors is that their resistances tend to be constant within their standard operating ranges. If 1 ampere and 2 amperes are both within a resistor's operating range then its resistance is going to be pretty much the same, much like 24 Gauge copper wire.

But let's suppose it's not. Let's suppose you want to find out what the resistance of your imperfect conductor is. That's easy to solve. All you need is Ohm's Law.

$$V=IR$$

$V$ is voltage. $I$ is current. $R$ is resistance. If voltage is fixed and the current is doubled then resistance is halved. If resistance is fixed and the current is doubled then voltage is halved.

So there's your answer. Did you double the current by modifying the voltage or modifying the imperfect conductor? If the former and your conductor behaves like a resistor then the conductor's resistance stays the same. If the latter then your conductor's resistance has just halved.

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You state the material carrying the current is a “conductor”. That would normally imply metal. But as @Isusr has already pointed out, 10 ohms would involve a very long and thin wire to achieve that resistance in the case of copper conductors.

That being said, the resistivity of an electrical conductor is a function of temperature. For metallic conductors, the resistivity ($ρ$) and resistance ($R$) can be considered to vary linearly with changes in temperature according to the following relationships, for a given temperature range:

$$ρ=ρ_{0}[1+α(T-T_{0})]$$

$$R=R_{0}[1+α(T-T_{0})]$$

where

$ρ_0$ = resistivity at $T_0$

$R_0$ = resistance at $T_0$

$α$ = temperature coefficient

For a conductor of given resistance R, we know that the power dissipated in the conductor is given by

$$P=I^{2}R$$

Increasing current increases power dissipation, which increases the temperature of the conductor and thus increases its resistance. Whether or not this is a practical concern with respect to electrical conductors is another matter. Consider the following example:

We have 400 feet (122 m) of 27 gauge copper wire which @Isusr says would have a resistance of 10 Ohms (presumably at room temperature). For copper we have:

$$α=\frac {4.29 x 10^{-3}}{^0C}$$ $$ρ_{0}= 1.724 x 10^{-8} Ohm-m$$

A temperature rise of 75 C increases its resistivity to $2.278x10^{-8}$ Ohm-m. If this temperature rise exists over the entire 122 m length of conductor, the resistance $R$ of the conductor will rise from 10 Ohms to about 13 Ohms.

Now let’s consider the possibility of getting this temperature rise over the entire conductor if we increase the current from 1 ampere to 2 amperes, assuming the conductor is laid out straight (as opposed to being coiled up). If I did my calculations correctly, this increases the power dissipation from 10 watts to 40 watts, or a 30-watt increase over the entire length. This is an increase of 0.0065 watts/inch. I should think that such a small increase in dissipation per unit length would result in a negligible temperature rise.

But if we had a coil of wire, the situation would be quite different as the watt density (watts per unit volume) would be much higher.

Hope this helps.

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Resistance of a particular resistor is fixed. However, it depends on the material the resistor is made of. The resistance offered by the resistor is also affected by the temperature of the resistor at the time of usage. The resistance of a given resistor varies directly with temperature.

Keeping temperature constant, the value of resistance is given by $R=\frac{V}{I}$, which is the famous Ohm's Law. What will change when the current changes is the Voltage, (or I should say what "causes" the change in current) is the voltage since you can change the current only by changing the Voltage across it for a particular resistor at a particular temperature.

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Resistance is a property of a material in which conduction occur and is dependent on temperature. Resistance remains same, doesn't matter if we increase current of some Ohmic devices. But voltage varies. We had defined Ohms law as voltage is directly proportional to the current given the temperature remains same. The constant which equates the proportionality is actually called Resistance.
Of course, resistance will vary with temperature. As time goes on the increase in temperature of the conductor may cause, change in resistance, but by a negligible amount.

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