• Support PF! Buy your school textbooks, materials and every day products Here!

Voltage, Current, Resistance Relationship

  • Thread starter Air
  • Start date
  • #1
Air
202
0
So I know [itex]V=IR[/itex] but can someone tell me which elements are proportional to each other?

...I believe current in inversely proportional to resistance but what about current and voltage. Also, what about voltage and resistance?
 

Answers and Replies

  • #2
Hootenanny
Staff Emeritus
Science Advisor
Gold Member
9,622
6
So I know [itex]V=IR[/itex] but can someone tell me which elements are proportional to each other?

...I believe current in inversely proportional to resistance but what about current and voltage. Also, what about voltage and resistance?
When we say x is proportional to y, this means we can write it in this form,

[tex]x = k\cdot y[/tex]

Where k is the constant of proportionality. When we say x is inversely proportional to y, we can write it in this form,

[tex]x = \frac{k^\prime}{y}[/tex]

Where k' is another constant of proportionality.

Now taking your example of current and resistance, you are indeed correct to say that current is inversely proportional to resistance because we can re-write Ohm's law thus,

[tex]I = \frac{V}{R}[/tex]

So in this case, V is our constant of proportionality.

Does that help to clear things up?
 
  • #3
Air
202
0
When we say x is proportional to y, this means we can write it in this form,

[tex]x = k\cdot y[/tex]

Where k is the constant of proportionality. When we say x is inversely proportional to y, we can write it in this form,

[tex]x = \frac{k^\prime}{y}[/tex]

Where k' is another constant of proportionality.

Now taking your example of current and resistance, you are indeed correct to say that current is inversely proportional to resistance because we can re-write Ohm's law thus,

[tex]I = \frac{V}{R}[/tex]

So in this case, V is our constant of proportionality.

Does that help to clear things up?
So is it:

Voltage is proportional to resistance.
Voltage is proportional to current.

:confused:
 
  • #4
Hootenanny
Staff Emeritus
Science Advisor
Gold Member
9,622
6
So is it:

Voltage is proportional to resistance.
Voltage is proportional to current.

:confused:
Indeed it is :approve:.
 
  • #5
Air
202
0
When a circuit short-circuits, does that mean current is zero hence resistance is low?
 
  • #6
Hootenanny
Staff Emeritus
Science Advisor
Gold Member
9,622
6
When a circuit short-circuits, does that mean current is zero hence resistance is low?
The resistance is indeed usually low, but that doesn't mean that the current is low, in fact it's quite the opposite. A short-circuit simply means that the current flows along an unintended path. In practise this usually means that a low-impedance connection is made between two points in the circuit that would normally be at difference voltages. Since the resistance is low, this causes a large current to flow across the short.
 
  • #7
Air
202
0
The resistance is indeed usually low, but that doesn't mean that the current is low, in fact it's quite the opposite. A short-circuit simply means that the current flows along an unintended path. In practise this usually means that a low-impedance connection is made between two points in the circuit that would normally be at difference voltages. Since the resistance is low, this causes a large current to flow across the short.
So, what about current? It's proportional to both so would it be high or low?
 
  • #8
Hootenanny
Staff Emeritus
Science Advisor
Gold Member
9,622
6
So, what about current? It's proportional to both so would it be high or low?
The resistance is indeed usually low, but that doesn't mean that the current is low, in fact it's quite the opposite. A short-circuit simply means that the current flows along an unintended path. In practise this usually means that a low-impedance connection is made between two points in the circuit that would normally be at difference voltages. Since the resistance is low, this causes a large current to flow across the short.
[tex]I = \frac{V}{R}[/tex]

The current is proportional to the voltage (which in this case is constant) and inversely proportional to the resistance, hence a low resistance results in a large current.
 
  • #9
Air
202
0
[tex]I = \frac{V}{R}[/tex]

The current is proportional to the voltage (which in this case is constant) and inversely proportional to the resistance, hence a low resistance results in a large current.
...And high voltage as it is proportional to current?
 
  • #10
Hootenanny
Staff Emeritus
Science Advisor
Gold Member
9,622
6
...And high voltage as it is proportional to current?
It isn't quite that simple, it would depend on the structure of the circuit.

It would perhaps be prudent to mention that the majority of shorts are not Ohmic conductors, since a very large current flows that short (wire) usually heats up very quickly and therefore there is a non-linear relationship between V, R and I.
 
Last edited:

Related Threads for: Voltage, Current, Resistance Relationship

Replies
1
Views
1K
  • Last Post
Replies
2
Views
2K
Replies
28
Views
4K
Replies
10
Views
51K
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
7
Views
906
  • Last Post
Replies
6
Views
2K
Replies
4
Views
27K
Top