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Which of the following two sentences is grammatically more appropriate? If the sentence needs commas, do also let me know.

"The analysis shows that the most important parameter affecting conductor temperature and hence power was the ambient temperature."

"The analysis shows that the most important parameter affecting the conductor temperature and hence the power was the ambient temperature."

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I'd keep the first sentence. "The" is a definite article, you should use that to emphasize a certain noun in the sentence and make it "unique" so to say. Over-using it will take its emphasizing power away.

Breakdown of your sentence:

"The analysis shows that the most important parameter..." - the "the" is there to emphasize this specific parameter over the others

"...affecting conductor temperature..." - in infer from context that we're talking about an already predefined conductor or about conductors in general, so there is no need to make a distinction between one specific conductor over others, or one specific conductor temperature over others

"and hence power was the ambient temperature" - again I'm inferring from context that you're talking about either a predefined power or a generic power. In this part I'd also remove the "the" preceding "ambient temperature" as I don't see value in making this stand out from the rest of the sentence.

The second sentence reads a little bit like it was written first in a Latin language and then translated due to the extensive use of definite articles preceding the direct objects.

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