Ohm's Law graphing inversed gradient value

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SUMMARY

This discussion centers on Ohm's Law and the graphical representation of resistance. When plotting voltage (V) on the x-axis and current (I) on the y-axis, the gradient (m) of the resulting linear trend line represents the inverse of resistance (R), leading to the equation I = mV + c. To find the true resistance value, the gradient must be inversed, resulting in R = 1/m. This inversion is essential for accurately calculating resistance from the slope of the voltage-current graph.

PREREQUISITES
  • Understanding of Ohm's Law and its components (voltage, current, resistance).
  • Familiarity with linear equations and graphing techniques.
  • Knowledge of how to interpret slope in a graph.
  • Basic skills in using graphing tools or software for plotting data.
NEXT STEPS
  • Study the relationship between voltage and current in ohmic devices.
  • Learn how to graph linear equations and interpret their slopes.
  • Explore the concept of inverse functions in mathematics.
  • Investigate practical applications of Ohm's Law in electrical engineering.
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Students studying physics, electrical engineers, and anyone interested in understanding the principles of Ohm's Law and resistance calculations.

Casius
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Homework Statement
Hey all. This is about Ohm's Law (and specifically resistance). When you plot the change in current vs the change in voltage you should get a linear trend line (providing it is from an ohmic device). The gradient should be the resistance. My questions is why does the gradient value need to be inversed to find the true resistance value?
Relevant Equations
y = mx +c
Hey all. This is about Ohm's Law (and specifically resistance). When you plot the change in current vs the change in voltage you should get a linear trend line (providing it is from an ohmic device). The gradient should be the resistance. My questions is why does the gradient value need to be inversed to find the true resistance value?
 
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Casius said:
Homework Statement:: Hey all. This is about Ohm's Law (and specifically resistance). When you plot the change in current vs the change in voltage you should get a linear trend line (providing it is from an ohmic device). The gradient should be the resistance. My questions is why does the gradient value need to be inversed to find the true resistance value?
Relevant Equations:: y = mx +c
Of voltage and current, which are you plotting as y and which as x?
 
haruspex said:
Of voltage and current, which are you plotting as y and which as x?
Voltage x, current y
 
Casius said:
Voltage x, current y
So you have I=mV+c.
What would m be there?
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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