# Voltage, Current, Resistance Relationship

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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Hootenanny
Staff Emeritus
Gold Member
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?

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. Hootenanny
Staff Emeritus
Gold Member
So is it:

Voltage is proportional to resistance.
Voltage is proportional to current. Indeed it is .

When a circuit short-circuits, does that mean current is zero hence resistance is low?

Hootenanny
Staff Emeritus
Gold Member
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.

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?

Hootenanny
Staff Emeritus
Gold Member
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.
$$I = \frac{V}{R}$$

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.

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

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?

Hootenanny
Staff Emeritus