# Definition of resistance

## Homework Statement

What is the definition of resistance?
a. Resistance is the potential difference per unit current
b. Resistance is the gradient of the graph of potential difference against current
c. Resistance is the voltage required for a current of 1 A
d. Resistance is defined by the equation R = ρL / A, where ρ is the resistivity of the material, L is the length of the wire and A is its cross sectional area
e. Resistance is the quantity that measure the ability of material to resist the current

## The Attempt at a Solution

I think the answer is between (d) or (e)

(d) is the equation that is used to define resistance and (e) is the meaning of resistance physically (maybe). How to determine which one is correct?

Thanks

haruspex
Homework Helper
Gold Member
2020 Award
Seems to me that while (e) is true it cannot constitute a definition since it gives no standard way to determine its value.
For (d), defining resistance in terms of resistivity gives you a problem when defining resistivity. You will go round in circles.

According to https://en.wikipedia.org/wiki/Electrical_resistance_and_conductance: "The resistance (R) of an object is defined as the ratio of voltage across it (V) to current through it (I),"

songoku
Seems to me that while (e) is true it cannot constitute a definition since it gives no standard way to determine its value.
So definition should involve standard way to calculate the value?

For (d), defining resistance in terms of resistivity gives you a problem when defining resistivity. You will go round in circles.
Then the equation is more appropriate to be used to define resistivity?

Thanks

haruspex
Homework Helper
Gold Member
2020 Award
definition should involve standard way to calculate the value?
If not, it is not much use as a definition. Two physicists would likely disagree over resistance values.
the equation is more appropriate to be used to define resistivity?
Yes. Think about the practicalities. How would you measure resistivity other than by measuring resistances of samples?

songoku and lekh2003
My friend found this question:

Which equation is used to define resistance?
A energy = (current)2 × resistance × time
B potential difference = current × resistance
C power = (current)2 × resistance
D resistivity = resistance × area ÷ length

He said the answer key wrote (D) as the answer. So the answer key is wrong and the correct answer should be (B)?

haruspex
Homework Helper
Gold Member
2020 Award
My friend found this question:

Which equation is used to define resistance?
A energy = (current)2 × resistance × time
B potential difference = current × resistance
C power = (current)2 × resistance
D resistivity = resistance × area ÷ length

He said the answer key wrote (D) as the answer. So the answer key is wrong and the correct answer should be (B)?
Yes. D defines resistivity.

songoku
Thanks a lot for your help

haruspex
Homework Helper
Gold Member
2020 Award
Thanks a lot for your help
Ok.
Do you understand the difference between a and b, and between a and c?

songoku
Ok.
Do you understand the difference between a and b, and between a and c?

Actually I don't really give thought at first for option (b) and (c) because I think it is impossible to be the definition but now you ask about it....I am not sure what the difference is between those three.

a. Resistance is the potential difference per unit current --> R = V / I

b. Resistance is the gradient of the graph of potential difference against current --> R = ΔV / ΔI

c. Resistance is the voltage required for a current of 1 A --> maybe more appropriate for definition of 1 ohm, not resistance?

By definition of R, it can not be stated as R = ΔV / ΔI but must be R = V / I so (b) is wrong?

Thanks

haruspex