# Voltage, Current, Resistance Relationship

by Air
Tags: current, relationship, resistance, voltage
 PF Patron P: 206 So I know $V=IR$ 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?
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 Quote by Air So I know $V=IR$ 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,

$$x = k\cdot y$$

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

$$x = \frac{k^\prime}{y}$$

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,

$$I = \frac{V}{R}$$

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

Does that help to clear things up?
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P: 206
 Quote by Hootenanny When we say x is proportional to y, this means we can write it in this form, $$x = k\cdot y$$ Where k is the constant of proportionality. When we say x is inversely proportional to y, we can write it in this form, $$x = \frac{k^\prime}{y}$$ 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, $$I = \frac{V}{R}$$ 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.

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P: 9,789

## Voltage, Current, Resistance Relationship

 Quote by Air So is it: Voltage is proportional to resistance. Voltage is proportional to current.
Indeed it is .
 PF Patron P: 206 When a circuit short-circuits, does that mean current is zero hence resistance is low?
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P: 9,789
 Quote by Air 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.
PF Patron
P: 206
 Quote by Hootenanny 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?
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P: 9,789
 Quote by Air So, what about current? It's proportional to both so would it be high or low?
 Quote by Hootenanny 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.
$$I = \frac{V}{R}$$

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.
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P: 206
 Quote by Hootenanny $$I = \frac{V}{R}$$ 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?
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 Quote by Air ...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.

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