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I would like some help in understanding the following contour plot. Contour plot of Ambient Temperature Vs Current in a conductor

I can see that as the ambient temperature increases the conductor temperature increases. I can also see that as the current through the conductor increases the temperature of the conductor increases.

I would like to know how to use the contour line to interpret some understanding of the plot. The contour lines are lines of same conductor temperature. Can I make a comment on the sensitivity of the conductor temperature to ambient temperature or current by looking at the contour lines? In general I would like to extract as mush useful understanding as I can from the plot.

Please advise

user401393
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1 Answers1

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Look at the contour line for $9^{\circ}C$.

The slope of the contour line at low current is very steep, meaning that the conductor temperature is mostly affected by ambient temperature at low current.

But as current increases, in order to maintain $9^{\circ}C$, the surroundings must cool more and more, hence why the contour becomes more horizontal than it was at $0A$, meaning current begins to take over what determines the conductor's temperature.

This is true for the rest of the lines, as they share similar shapes and the spacing between them stays relatively constant.

Also, look at the $99^{\circ}C$ contour line. Based on the pattern of those intercepts we can see, it likely intercepts ambient temperature somewhere around $95^{\circ}C$ and as current nears the top, the ambient temperature must drop about $75^{\circ}C$ just for it to stay at $99^{\circ}C$. Compare this to the $69^{\circ}C$ contour line, which intercepts at about $65^{\circ}C$. As current maxes out, the surroundings must cool by about $70^{\circ}C$, a decrease by $5^{\circ}C$.

mallan
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  • Thanks for the explanation. So, it would be wise to say that at lower currents the conductor temperature is sensitive to ambient temperature while at higher currents, the current dominates the conductor temperature? – user401393 May 08 '18 at 00:30
  • Exactly! You can see it in the plot another way. Pick an ambient temperature, $0C$, and look vertically up and notice how the spacing between each contour line decreases as current increases. – mallan May 08 '18 at 01:23