# Homework Help: Voltage, Current, Resistance Relationship

1. May 22, 2008

### 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?

2. May 22, 2008

### Hootenanny

Staff Emeritus
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?

3. May 22, 2008

### Air

So is it:

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

4. May 22, 2008

### Hootenanny

Staff Emeritus
Indeed it is .

5. May 22, 2008

### Air

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

6. May 22, 2008

### Hootenanny

Staff Emeritus
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. May 22, 2008

### Air

So, what about current? It's proportional to both so would it be high or low?

8. May 22, 2008

### Hootenanny

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

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.

9. May 22, 2008

### Air

...And high voltage as it is proportional to current?

10. May 23, 2008

### Hootenanny

Staff Emeritus
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: May 23, 2008