# Voltage, Current, Resistance Relationship

• Air
In summary, current and voltage are directly proportional to each other, while current and resistance are inversely proportional to each other. A short-circuit can result in a large current flow due to the low resistance, but the specific relationship between current and voltage would depend on the circuit structure.
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?

Air said:
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?

Hootenanny said:
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.

Air said:
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?

Air said:
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.

Hootenanny said:
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?

Air said:
So, what about current? It's proportional to both so would it be high or low?
Hootenanny said:
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.

Hootenanny said:
$$I = \frac{V}{R}$$

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?

Air said:
...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:

## What is the relationship between voltage, current, and resistance?

The relationship between voltage, current, and resistance is known as Ohm's Law. It states that the current through a conductor between two points is directly proportional to the voltage across the two points, and inversely proportional to the resistance between them.

## What is voltage?

Voltage is the measure of the electric potential energy per unit charge. It is commonly referred to as the force that pushes electrons through a conductor. Voltage is measured in volts (V) and is represented by the symbol "V" in equations.

## What is current?

Current is the flow of electric charge through a conductor. It is measured in amperes (A) and is represented by the symbol "I" in equations. Current flows from high voltage to low voltage.

## What is resistance?

Resistance is the measure of how difficult it is for current to flow through a material. It is measured in ohms (Ω) and is represented by the symbol "R" in equations. Resistance can be affected by factors such as the material, length, and thickness of the conductor.

## How are voltage, current, and resistance related in a circuit?

In a circuit, voltage is directly proportional to current and inversely proportional to resistance. This means that if voltage increases, current will also increase, but if resistance increases, current will decrease. This relationship is described by Ohm's Law, V=IR.

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