Which equation is used to define resistance?

In summary, resistance is defined as the ratio of voltage across an object to the current through it. This can be calculated using the equation R = V / I. Other definitions, such as using the gradient of a graph or specifying a specific voltage and current, are not considered accurate definitions of resistance. The equation R = ρL / A may be used to define resistivity, but it should not be used to define resistance.
  • #1
songoku
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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
 
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  • #2
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),"
 
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  • #3
haruspex said:
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
 
  • #4
songoku said:
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.
songoku said:
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?
 
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  • #5
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)?
 
  • #6
songoku said:
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.
 
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  • #7
Thanks a lot for your help
 
  • #8
songoku said:
Thanks a lot for your help
Ok.
Do you understand the difference between a and b, and between a and c?
 
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  • #9
haruspex said:
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
 
  • #10
songoku said:
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.
songoku said:
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.
 
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  • #11
Thank you very much for your help
 

What is resistance?

Resistance is a measure of how much a material or object opposes the flow of electric current. It is measured in ohms (Ω) and is determined by the material's electrical properties, such as conductivity and temperature.

What are the factors that affect resistance?

The factors that affect resistance include the material's electrical properties, such as conductivity and temperature, as well as the length and cross-sectional area of the material. The type and size of the conductor also play a role in determining resistance.

How does resistance impact electric circuits?

Resistance is a crucial component in electric circuits as it limits the flow of current in a circuit. It also causes a voltage drop, which is necessary for the proper functioning of various components in the circuit. Without resistance, the current would be too high and could potentially damage the circuit.

What is the difference between resistance and impedance?

Resistance is a measure of the opposition to current flow in a DC circuit, while impedance is a measure of the opposition to current flow in an AC circuit. Impedance takes into account both resistance and reactance (the opposition to current flow caused by capacitance and inductance).

How is resistance calculated?

Resistance is calculated using Ohm's Law, which states that resistance (R) is equal to the voltage (V) divided by the current (I). In mathematical terms, this can be expressed as R = V/I. Additionally, resistance can also be calculated using the formula R = ρL/A, where ρ is the resistivity of the material, L is the length of the material, and A is the cross-sectional area of the material.

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