Calculating resistance from a graph

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Discussion Overview

The discussion revolves around calculating the resistance of a resistor and a lamp using a graph that plots voltage against current. Participants explore the implications of Ohm's law, particularly in the context of linear versus non-linear relationships in electrical components.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant notes that for the resistor, the relationship is linear, allowing the use of the gradient to determine resistance directly from the graph.
  • Another participant points out that for the lamp, which exhibits a non-linear relationship, the gradient does not equate to V/I, raising questions about the application of Ohm's law.
  • A later reply suggests that to find resistance at a specific point on the non-linear graph, one should calculate ΔV/ΔI at that operating point.
  • Some participants argue that this approach does not contradict Ohm's law, as Ohm's law is traditionally applied to linear components and can be generalized to non-linear cases through the concept of impedance.
  • It is mentioned that Ohm's law describes behavior under specific conditions, and resistance can vary with voltage in non-linear components.
  • Another participant emphasizes that in practical applications, non-linear components can often be treated as having a constant resistance over small signal ranges.

Areas of Agreement / Disagreement

Participants express differing views on the application of Ohm's law to non-linear components, with some asserting that there is no contradiction while others highlight the complexities involved. The discussion remains unresolved regarding the implications of resistance calculations for non-linear devices.

Contextual Notes

Participants acknowledge that the definition of resistance as V/I may not hold for non-linear components, and the discussion includes considerations of temperature effects and the generalization of Ohm's law.

JizzaDaMan
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Hi, i have a graph with voltage (y axis) plotted against current (x axis) and I need to calculate the resistance of a resistor and a lamp from this.

My physics teacher has told me that by Ohm's law, R = V/I, and he has also told me that on the graph, the resistance is the gradient of the graph.

The graph for the resistor is linear, so V/I is the same as the gradient, I have no problem with this. However, the graph for the lamp is non linear, so V/I isn't the same as the gradient.

What's the correct answer here? Am I missing something blindingly obvious? Thanks for any help
 
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JizzaDaMan said:
Hi, i have a graph with voltage (y axis) plotted against current (x axis) and I need to calculate the resistance of a resistor and a lamp from this.

My physics teacher has told me that by Ohm's law, R = V/I, and he has also told me that on the graph, the resistance is the gradient of the graph.

The graph for the resistor is linear, so V/I is the same as the gradient, I have no problem with this. However, the graph for the lamp is non linear, so V/I isn't the same as the gradient.

What's the correct answer here? Am I missing something blindingly obvious? Thanks for any help

Good question. You would need to figure out what the operating point is (what current are you running at -- what point are you at on the graph?), and use ΔV/ΔI at that point. Does that make sense?
 
It makes perfect sense to me :D but what doesn't is that if I calculate the gradient at that point, it isn't the same as V/I. surely this contradicts Ohm's law?
 
JizzaDaMan said:
It makes perfect sense to me :D but what doesn't is that if I calculate the gradient at that point, it isn't the same as V/I. surely this contradicts Ohm's law?

Why do you say that? And don't call me Shirley.
 
Well if the resistance of the lamp is ΔV/ΔI at any point on the graph, then given that the relationship between the voltage and current for the lamp is non-linear, this will not be V/I which by Ohm's law is the formula for resistance.
 
JizzaDaMan said:
Well if the resistance of the lamp is ΔV/ΔI at any point on the graph, then given that the relationship between the voltage and current for the lamp is non-linear, this will not be V/I which by Ohm's law is the formula for resistance.

The original definition of Ohms Law was just the linear equation V=IR. But it can be generalized to describe an Impedance Z which is ∂V/∂I. This is used all the time in EE. We talk about the "Impedance at a point" pretty frequently (because there are many non-linear circuits that you will work with...).
 
Ohm's Law only describes the behaviour of a metal at constant temperature. That's all. The Resistance of a component is defined as V/I but, of course, as V changes, this WILL change for a non-linear component (by definition).
There is no violation of any law here because Ohm's Law is not really a physical 'Law', in any case - it is just an observation of how a certain material tends to behave under given conditions.
For 'small signals', many non-linear components behave as if they have a 'resistance' because ∂V/∂I happens to be more or less constant over a particular range of V. So, under certain circumstances, we can assign a value for R and work with it.
EE does this all the time. We use 'current sources' and 'voltage sources' all the time and it works very well in practical terms and it's the same sort of thing. You must not let it spoil your day - just be glad that the system works so well.
 
Thank you guys, I'm pretty sure I understand that now :)
 

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