Understanding Ohm's Law: The Relationship between Resistance and Voltage

[hamburgler]

Ohm's Law Yay! :(

Homework Statement

1. How does the resistance of most objects vary with voltage?

Homework Equations

V=RI I=V/R

The Attempt at a Solution

They are independent of each other (resistance is a constant).

 

[Dick]

Your last two sentences are contradictory. If they are independent of each other, then they don't mutually increase. Which do you believe?

 

[hamburgler]

I changed it to read

They are independent of each other (resistance is a constant).

 

[montoyas7940]

I'm not sure if I understand you... Are you saying that the voltage drop of a series resistor increases as the source voltage increases? If so, you are correct.

Robble Robble

 

[Dick]

Then you are correct. For most substances, over some range of voltage, the resistance is approximately independent of voltage. Hence, 'Ohms law'. There are exceptions.

 

[rohanprabhu]

This is more or less a mathematical model. Resistance is 'constant' in most of the real world applications where we use Carbon resistors and such.

The formula:

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

means that 'R' is proportional to 'V' given that 'I' is constant. But, in real world practices, 'I' varies constantly with 'V'. Mathematically what this means is that, if 'V' is increased.. then to keep 'I' constant, 'R' must be increased proportionally to 'V'.

Some increases are phenomenal. Like the increase of current when voltage is increased under constant current. It happens all by itself with indirect intervention from you [you increased the voltage]. Other changes require the direct intervention of the observer. Mathematics doesn't take into account who or what causes the change. Proportionality is a study of relation of changes, no matter what causes it.

Take the case when you have a rheostat in your circuit. You need to change the 'R' here everytime 'V' is changed to ensure that 'I' is constant. And when you do this for various values for 'V' and 'R' such that 'I' is kept constant for each step of the way.. you'll see that 'V' is proportional to 'R'.

Hope that helps.

 

[hamburgler]

Thanks :D