Which equation is used to define resistance?

[songoku]

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

Homework Equations

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]

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]

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]

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]

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]

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]

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

Yes. This is a useful concept, but would be better termed, say, marginal resistance. Actual resistance might not be constant across a range of voltages.

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

Exactly. It goes too far by specifying the unit.

 

[songoku]

Thank you very much for your help