Why is the gradient of a V-I graph equal to resistance for ohmic materials?

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The gradient of a voltage-current (V-I) graph for ohmic materials represents resistance, as it reflects the change in voltage over the change in current. For these linear resistances, the gradient is consistent and equal to the ratio of voltage (V) to current (I) at any point on the graph. This relationship holds true because ohmic materials obey Ohm's Law, where resistance remains constant regardless of the voltage or current levels. Thus, the resistance can be accurately described as both the gradient and the ratio V/I. Understanding this concept is crucial for analyzing electrical circuits involving ohmic materials.
Cici2017

Homework Statement


Is the resistance equal to V/I at any point, or is it the gradient at that point? And Why?

Homework Equations

The Attempt at a Solution


shouldn't it be the gradient? because it is change in V over change in I?

Thanks~
 
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Cici2017 said:
shouldn't it be the gradient? because it is change in V over change in I?
Yes, it's the gradient. But for ohmic materials (linear resistances), the gradient is same as V/I.
Can you say why?
 
cnh1995 said:
Yes, it's the gradient. But for ohmic materials (linear resistances), the gradient is same as V/I.
Can you say why?
Yes =) Thanks for making it clear :blushing:
 
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