What is the Relationship Between Resistance and Current in a Resistor?

[lha08]

Homework Statement

I'm confused because in my textbook, it says that when R is large, there is very little current and if it is small, there is more current through it when there's a potential difference across the resistor...but like in another book, it says that current is not used up when current flows through the resistor, that the number of charges that leave one terminal of the battery is exactly equal to the number that enter via the other terminal...it seems kind of contradictory...maybe I'm just misunderstanding it, but which explanation makes more sense?

Homework Equations

The Attempt at a Solution

 

[ideasrule]

There's no contradiction. If R is small, maybe 3 C go into the resistor per second; then 3C will have to go out per second. If R is big, maybe 0.5C go in per second, in which case 0.5C would have to leave.

 

[lha08]

There's no contradiction. If R is small, maybe 3 C go into the resistor per second; then 3C will have to go out per second. If R is big, maybe 0.5C go in per second, in which case 0.5C would have to leave.

But then how is it that when current is passing in a circuit with 2 resistors, how does it manage to alternate between let's say providing 0.5 C to one resistor and right after it with 3 C to another resistor?

 

[kuruman]

They both make sense. When charges flow through a resistor, the resistor is always electrically neutral. This means that what goes in must come out. If that were not the case, then charges would accumulate in the resistor and the resistor would no longer be electrically neutral.

As for the increasing resistance situation, think of water flowing through a pipe that is plugged with, say, a washcloth. To drive water through the pipe you need higher pressure at one end than the other. Pressure difference here is the equivalent of potential difference and water flow the equivalent of electrical current. So, if you increase the "resistance" by plugging the pipe with two washcloths, you will need more pressure difference (voltage) to get the same water flow (current). Nevertheless, whatever amount of water comes in one end must come out the other, else water will be accumulating inside the pipe.

 

[lha08]

They both make sense. When charges flow through a resistor, the resistor is always electrically neutral. This means that what goes in must come out. If that were not the case, then charges would accumulate in the resistor and the resistor would no longer be electrically neutral.

As for the increasing resistance situation, think of water flowing through a pipe that is plugged with, say, a washcloth. To drive water through the pipe you need higher pressure at one end than the other. Pressure difference here is the equivalent of potential difference and water flow the equivalent of electrical current. So, if you increase the "resistance" by plugging the pipe with two washcloths, you will need more pressure difference (voltage) to get the same water flow (current). Nevertheless, whatever amount of water comes in one end must come out the other, else water will be accumulating inside the pipe.

So let me see if i understand it, if there's a current first passing through a resistor with a high resistance, the current through it will be small then there will be a low potential difference that will be needed in order equal to current that first passed through (will they lose potential energy?), and if it then passed through a resistor with a low resistance, then it needs a high potential difference so that the same current in the circuit is maintained (will it gain potential energy?)??

 

[tkwan]

It depends on how you have your resistors arranged. If you have two resistors in series with a source, then you will have the SAME current through both resistors. If your resistors are in series then you have different currents through them.

 

[kuruman]

So let me see if i understand it, if there's a current first passing through a resistor with a high resistance, the current through it will be small then there will be a low potential difference that will be needed in order equal to current that first passed through (will they lose potential energy?), and if it then passed through a resistor with a low resistance, then it needs a high potential difference so that the same current in the circuit is maintained (will it gain potential energy?)??

Ohm's Law says V = IR, potential difference = current times resistance. Fix the potential difference at, say, 12 Volts what a car battery provides. If you connect a 1 Ohm resistor to that battery you will get 12 Amps of current; if you connect a 2 Ohm resistor, you get 6 Amps of current; if you connect a 4 Ohm resistor you get 3 Amps of current and so on.

Charge carriers moving through a resistor always lose potential energy when they emerge through the other end, yet their kinetic energy remains unchanged. The lost potential energy is converted into heat (that's how a toaster works) or heat and mechanical work (that's how an electric motor works).