What factors influence voltage

[Arcthor]

I have some trouble grasping voltage, and why it is defined by V = R * I.

1. If voltage can be seen as some form of electrical potential energy, why does it not increase as the circuit is made longer (in terms of meters). Would a current be as likely to travel in a 0.1 meter circuit as in a 100000000000000 meter circuit given the same resistance?

2. Why does increased resistance result in an increased voltage? Would it not be the opposite to this? The harder it is to do something, the less nature wants to do it right?

3. When I've got a standard 9 volt battery, is that the emf of the battery? Does the actual number of volts I can get out of the battery differ from this number since every conductor has resistance?

 

[stedwards]

Forget about it.

It's perfectly fine for initial understanding to think of electrical circuits as water flowing in pipes, and it can serve you for a long time.

Voltage can be thought of as how much pressure is at a location in a pipe. Current is analogous to the amount of water passing in a section of pipe. The sand resists the flow of water. A resistor resists the flow of current.

A resistor is some section of pipe full of sand that won't be carried along with flow. It takes a pressure difference (voltage difference) across the sandy section to get the water (current) to flow through the sand.

 

[axmls]

1. It's important not to confuse electrical potential (voltage) with electrical potential energy. If the two circuits in your example have the same resistance, and the same voltage drop across them, then they will have the same current.

2. Look at what you're holding constant here. You say that if you increase the resistance, the voltage will rise. But that's only if you're holding the current I constant in Ohm's law. But the current isn't constant if you're using a voltage source--it depends on the load. Rather, the voltage is constant, and as you raise the resistance, then the current will drop accordingly. (If you have a current source, then I will be constant, and an increased resistance will yield a higher voltage drop)

3. An ideal 9 V battery will output exactly 9 V, but all batteries have internal resistances, and things change with temperature and whatnot (batteries can get complicated), and so it's usually less than 9 V.

 

[davenn]

2. Why does increased resistance result in an increased voltage? Would it not be the opposite to this? The harder it is to do something, the less nature wants to do it right?

not quite correct

note carefully what axmls said for #2

making the resistor value larger doesn't increase the voltage. That is it cannot become greater than the voltage source
a resistor across a voltage source will always drop the full value of the voltage. What is going to increase is the current flowing
large value resistance = small current, small value resistance = large current

OK have a look at these circuits I have drawn ...
one is a 10 Ohm resistor the other a 1000 Ohm resistor

4 questions for you to answer
1) what is the voltage at the top of each resistor ?
2) what is the voltage as the bottom of each resistor ?
3) what do those answers tell you about what happens to the voltage across the resistor ?
4) what is the current flowing through each resistor ? ( use Ohms Law to solve)

cheers
Dave

 

[CWatters]

I have some trouble grasping voltage, and why it is defined by V = R * I.

It's not "defined" by V= IR. That just happens to be a useful equation in certain situations. Personally I also like the water analogy in which voltage is equivalent to the water pressure OR the pressure lost/gained passing through something.

2. Why does increased resistance result in an increased voltage?

It doesn't always. It depends on where you are measuring "V" in the circuit. For example V might be...

a) the voltage "lost" as a current flows through a resistor R (relevant equation V=IR) or
b) the voltage delivered to a load through wires that have resistance R (relevant equation V = Vsource - IR)

 

[Arcthor]

Forget about it.

It's perfectly fine for initial understanding to think of electrical circuits as water flowing in pipes, and it can serve you for a long time.

Voltage can be thought of as how much pressure is at a location in a pipe. Current is analogous to the amount of water passing in a section of pipe. The sand resists the flow of water. A resistor resists the flow of current.

A resistor is some section of pipe full of sand that won't be carried along with flow. It takes a pressure difference (voltage difference) across the sandy section to get the water (current) to flow through the sand.

Thank you for your answer! I really like the analogy, however, I find it hard to do the math if I do not understand why it happens.

1. It's important not to confuse electrical potential (voltage) with electrical potential energy. If the two circuits in your example have the same resistance, and the same voltage drop across them, then they will have the same current.

2. Look at what you're holding constant here. You say that if you increase the resistance, the voltage will rise. But that's only if you're holding the current I constant in Ohm's law. But the current isn't constant if you're using a voltage source--it depends on the load. Rather, the voltage is constant, and as you raise the resistance, then the current will drop accordingly. (If you have a current source, then I will be constant, and an increased resistance will yield a higher voltage drop)

3. An ideal 9 V battery will output exactly 9 V, but all batteries have internal resistances, and things change with temperature and whatnot (batteries can get complicated), and so it's usually less than 9 V.

Wow your answer to question 2 was really eye-opening, you cleared up a lot of confusion. Thank you!

not quite correct

note carefully what axmls said for #2

making the resistor value larger doesn't increase the voltage. That is it cannot become greater than the voltage source
a resistor across a voltage source will always drop the full value of the voltage. What is going to increase is the current flowing
large value resistance = small current, small value resistance = large current

OK have a look at these circuits I have drawn ...
one is a 10 Ohm resistor the other a 1000 Ohm resistor

4 questions for you to answer
1) what is the voltage at the top of each resistor ?
2) what is the voltage as the bottom of each resistor ?
3) what do those answers tell you about what happens to the voltage across the resistor ?
4) what is the current flowing through each resistor ? ( use Ohms Law to solve)

View attachment 85110cheers
Dave

Thank you for a great answer, really appreciated. I don't think I fully grasp it though, excuse my ignorance. If the resistance cannot become greater than the voltage source, what would happen if I were to cram a thousand 10 ohm resistors on a 10 V circuit? Would the voltage drop for each resistor be the same, and would it be -0.001*1000*10? And if the resistors have different resistance, does each resistor drop the voltage to a value that corresponds to its resistance?

I tried answering your questions:

1) 10 V
2) 0 V
3) The total resistance drops the total voltage.
4) 1A and 0.01A

This raises two more questions for me though:
1. right after the resistance, there is 0 voltage and 0 resistance in the circuit. That gives an impossible value for the current no?
2. Why does the electrons want to finish the circuit if there is no potential left?

Is the current right before a resistance higher than after the resistance? Again, excuse my ignorance on the topic.

It's not "defined" by V= IR. That just happens to be a useful equation in certain situations. Personally I also like the water analogy in which voltage is equivalent to the water pressure OR the pressure lost/gained passing through something.

It doesn't always. It depends on where you are measuring "V" in the circuit. For example V might be...

a) the voltage "lost" as a current flows through a resistor R (relevant equation V=IR) or
b) the voltage delivered to a load through wires that have resistance R (relevant equation V = Vsource - IR)

Thank you for a great answer. So the voltage without accounting for interal resistance is the emf?

 

[davenn]

Thank you for a great answer, really appreciated. I don't think I fully grasp it though, excuse my ignorance. If the resistance cannot become greater than the voltage source,

that hilited bit doesn't make sense ... you can have a resistance of any value, into the millions of Ohms say a 22 MOhm (22 million Ohm) resistor

what would happen if I were to cram a thousand 10 ohm resistors on a 10 V circuit? Would the voltage drop for each resistor be the same, and would it be -0.001*1000*10? And if the resistors have different resistance, does each resistor drop the voltage to a value that corresponds to its resistance?

no ... now here comes a variation of the circuits I have shown above. with multiple resistors they can be arranged 2 ways ( or combinations there of)
1) series connection ... one resistor following another or 2) parallel connection resistors connected side by side

I will do a separate post describing those

I tried answering your questions:

1) 10 V
2) 0 V
3) The total resistance drops the total voltage.
4) 1A and 0.01A

well done !

This raises two more questions for me though:
1. right after the resistance, there is 0 voltage and 0 resistance in the circuit. That gives an impossible value for the current no?
2. Why does the electrons want to finish the circuit if there is no potential left?
3. Is the current right before a resistance higher than after the resistance? Again, excuse my ignorance on the topic.

1) ... no its not its just the point in common with the negative ( 0V) terminal of the battery or other power supply ... there needs to be a complete circuit from positive to negative (or visa-versa) for current to flow

2) ... The electrons ( since you used that term) flow from the negative (0V) terminal to the positive terminal ( conventional current flows the other way ... we won't get into that at the moment ... let's just assume the use of conventional current flow from positive to negative OK )

3) no it isnt

Dave

 

[davenn]

Ok let's look at series resistors across a voltage source

now this is a real easy one as the resistor values are the same
you can see that the 10V supply drops by 1/2 across each resistor ... ie a 5V drop across each one for a total of 10V

1) say the resistor values were different the top one 10 Ohms and the bottom one 100 Ohms, what then ?

then we approach it slightly differently we work out the current flowing in the circuit and with that info work out the voltage drop across each resistor

this is where your last question ... 3. Is the current right before a resistance higher than after the resistance? comes into play

the answer I gave was ... no, it isn't ... for a DC series circuit the current flowing is the same everywhere in the circuit

ie. in that top section of wire between the + terminal and the top of the first resistor ( at A), in the section marked as B and in the section from the bottom of the lower resistor, from C back to the negative terminal.
2) So, how do we work out the current flowing ? again use Ohms Law just like you did in the first circuit above ... I = voltage / total resistance

have a go and post your answer

once you have done that

then you can use the current to discover the voltage drop across the 10 Ohm and the 100 Ohm resistors in 1). above

have a goDave