# Relationship of voltage and resistance

by Googl
Tags: relationship, resistance, voltage
 P: 111 Would you say voltage drop across a resistor is directly proportional to the resistance. I am trying to understand the relationship between voltage and resistance. Thanks.
 Mentor P: 15,568 V=IR by Ohms law. So if you keep I fixed and vary R then you will indeed find that V is proportional to R.
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P: 6,345
 Quote by Googl Would you say voltage drop across a resistor is directly proportional to the resistance.
Yes. But that is just Ohm's law: V=IR. If you have several resistors connected in series, the current is the same through each. So the voltage drop across each resistor is directly proportional to R.

AM

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P: 1,812

## Relationship of voltage and resistance

But isn't all this just the definition of resistance?

There is no physics really in a definition.

There is some phenomenological physics in saying that in some common laboratory and technological situations (little else) resistance, so defined, is relatively independent of voltage and current. Up to a point. There is some simple physics I suppose - evidence of uniformity - with the (phenomenological) 'laws' of how it depends on the length and cross sectional area of uniform material. Though you can imagine situations and mechanisms where the simple laws break down
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P: 15,568
 Quote by epenguin But isn't all this just the definition of resistance? There is no physics really in a definition.
I agree. V is proportional to R if you keep I fixed precisely because R is defined as the ratio between V and I. No physics, just application of a definition.
 P: 111 Thanks a lot all of you, you've just strengthened my confidence in the idea. I know what voltage, current and resistance is but when put in certain scenarios it can be quite difficult to imagine, yes I understand the law is there but the imagination. To understand further the relationship of resistance with voltage, we would have to keep current constant and adjust the resistance and observe the voltage across the resistor (not emf). A variable resistor would be appropriate; Suppose I get a resistor that is adjustable from 0-20KΩ then I get a 20V battery and combine them together to form a circuit. My main goal is adjusting the resistance to observe what happens to the voltage across the resistor. How would you describe voltage when the resistance changes. Am I correct in saying that as the resistance increases the voltage across the resistor will be higher. Would you say that at 20KΩ the voltage across the resistor would be 20V? It is also quite had to imagine the ratio, I am thinking that I cannot just say that at 19KΩ the voltage would be 19V OR am I wrong? Also how would you describe the voltage across the resistor with the original voltage from the power supply (e.m.f)
 PF Patron P: 1,812 Noo. You are getting into a different question, the question of the supplies of voltage or current. A battery has an approximately constant voltage, so it's the current that mainly varies according to the resistance. Same thing with mains supply as usually engineered.
P: 111
 Quote by epenguin Noo. You are getting into a different question, the question of the supplies of voltage or current. A battery has an approximately constant voltage, so it's the current that mainly varies according to the resistance. Same thing with mains supply as usually engineered.
So when the emf is 20V and I connect it with a variable resistor, when I adjust the resistance to let's say 20KΩ and I put a voltmeter parallel to the variable resistor the voltmeter would read 20V? and when I change the resistance to 3KΩ the voltmeter would read 20V as well? I am referring to voltage drop across the resistor.
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P: 10,057
 Quote by Googl Would you say voltage drop across a resistor is directly proportional to the resistance. I am trying to understand the relationship between voltage and resistance. Thanks.
This is true but only true if a constant current is passed. In most cases (bulbs and batteries etc.) it is the voltage supplied that is constant. So beware; this relationship you seek will all depend upon the context.
If you just consider R as the ratio of V/I, you can't go far wrong.
 PF Patron Sci Advisor P: 2,555 Just thought I'd throw this in. http://hyperphysics.phy-astr.gsu.edu...ic/ohmlaw.html
 P: 111 Thanks for the illustration and link. I understand that. However this does not describe the relationship between the voltage measured across a resistor and it's resistance in my scenario above. Let's not focus on emf here just the voltage drop across the resistor. Suppose I use a variable resistor to contrast the resistance, connected to a source or battery that provides 20V. The variable resistor can be adjusted from 0KΩ to 20KΩ. What relationship would you observe when you connect a voltmeter in the circuit parallel to the variable resistor if you keep adjusting the variable resistor resistance? By my understanding is that as the resistance of the variable resistor is set to 20KΩ the voltmeter would read 20V (voltage drop) since resistance is directly proportional to voltage. But it would not make sense to say that when the resistance of the variable resistor is set to 0KΩ the voltage read from the resistor would be 0V. Am I missing something in the relationship here? If the above is true then this implies that the ratio between the two is a 1:1 ratio...
 PF Patron Sci Advisor P: 2,555 As the resistance approaches zero, the current would approach infinity. Do you know of any sources that can provide an infinite amount of power? In reality, power sources have "internal" resistance, so as the current increases, the voltage of the source lowers. http://hyperphysics.phy-astr.gsu.edu...ric/dcex6.html
 P: 111 Hello Don, I am referring to voltage drop across the resistor, not current and not the voltage, V of the source. The resistor is a sliding variable resistor. I am trying to understand the relationship of sliding the contact to adjust the resistance and the voltage across.
 PF Patron Sci Advisor P: 10,057 I seriously suggest that you don't try to 'look at it your way' because it really is a bit of a dead end. All you can say about the relationship between resistance and voltage is that R=V/I. That works everywhere because R is defined that way; it is just a ratio of two measurable quantities. If the resistance is ohmic or non ohmic then the relationship still applies - you have an instantaneous resistance which varies as a signal varies. If I asked you whether speed is proportional to distance then you would, rightly, say that it depends upon the time involved, too. It's the same for R and V.
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P: 10,057
 Quote by Googl Hello Don, I am referring to voltage drop across the resistor, not current and not the voltage, V of the source. The resistor is a sliding variable resistor. I am trying to understand the relationship of sliding the contact to adjust the resistance and the voltage across.
OK. Once you have decided on the value of your variable resistor then treat the network as a potential divider and do the sums to find the volts across it. These sums, of course,involve (implied) current and volts - the current being the same through each and volts being shared between the two resistors in proportion to the R values. BUT, it is the combination of the two resistors that determines the voltage across them and not a simple rule involving just one resistor. As I said ten miles back, it's a matter of context; there is not a relationship between just any old resistor on its own and the voltage across it.

If you want to "understand" what happens, do some calculations for yourself and plot values for a range of variable resistance values. The graph you get will show you what happens; you don't get a straight line for V against R.
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P: 1,812
 Quote by Googl Hello Don, I am referring to voltage drop across the resistor, not current and not the voltage, V of the source. The resistor is a sliding variable resistor. I am trying to understand the relationship of sliding the contact to adjust the resistance and the voltage across.
To a first approximation you will not change the voltage at all between (let me say it carefully as you may have some setup in your head) between the terminals of the battery by changing the resistance. Not because it is absurd to think, but because (approximately) constant voltage is a property of batteries. What you will change essentially by changing resistance is what you seem not to look at - the current!

All this is in any beginning textbook of physics that deals with current electricity.

Edit: "I am referring to voltage drop across the resistor, not current and not the voltage, V of the source." But the the voltage drop across the resistor when current flows is the voltage of the source. OK, so you connect the battery to the resistor through copper wires. These are excellent conductors - that's why they are used for wires - then, by Ohm's law already quoted, because their resistance is small there is negligible voltage drop across them so the voltage drop across the resistor is that of the battery.
P: 111
 Quote by sophiecentaur OK. Once you have decided on the value of your variable resistor then treat the network as a potential divider and do the sums to find the volts across it. These sums, of course,involve (implied) current and volts - the current being the same through each and volts being shared between the two resistors in proportion to the R values. BUT, it is the combination of the two resistors that determines the voltage across them and not a simple rule involving just one resistor. As I said ten miles back, it's a matter of context; there is not a relationship between just any old resistor on its own and the voltage across it. If you want to "understand" what happens, do some calculations for yourself and plot values for a range of variable resistance values. The graph you get will show you what happens; you don't get a straight line for V against R.
Thanks for this. This is what I was referring to.

 Quote by sophiecentaur it is the combination of the two resistors that determines the voltage across them and not a simple rule involving just one resistor
I am not so sure what you meant here. I have a variable resistor that is adjustable. The total resistance for this variable resistors is let's say 20KΩ.

Let's consider proportionality or ratio here. Never mind current it is just a constant value. It's just the ratio or proportionality for this situation.

Let's say I get a battery of 20V connected with a VARIABLE resistor with a sliding contact. The total resistance of this resistor is 20KΩ. I would like to imagine this ratio, for let's say where will I set the resistance to output the maximum voltage or what resistance value will I have to set to output a 10V
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