Inductive and capacitive reactance

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Capacitive reactance is subtracted from inductive reactance in overall reactance calculations due to the conventions established in electrical engineering, where inductive reactance is assigned a positive sign and capacitive reactance a negative sign. This convention reflects the physical behavior of circuits, with current leading voltage in capacitors and lagging in inductors. The formula for capacitive reactance is typically represented as Xc = 1/(ωC), where ω is the angular frequency and C is the capacitance. Understanding these conventions and maintaining rigorous arithmetic practices is essential for accurate calculations. Overall, the established signs simplify the algebra involved in circuit analysis.
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Why is it that capacitive reactance is subtracted from inductive reactance and not the other way around when determining the overall reactance?
 
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What is the formula for capacitive reactance?

With a j in the denominator, the term becomes negative when you bring it to the numerator.

Understand?
 
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fonz said:
Why is it that capacitive reactance is subtracted from inductive reactance and not the other way around when determining the overall reactance?
Reactances in series add. Inductive reactance has a + associated with it, and capacitive reactance has a – associated with it. They keep these signs when you add them, and the result can end up being a net + or a net – depending on the magnitudes.
 
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fonz said:
Why is it that capacitive reactance is subtracted from inductive reactance and not the other way around when determining the overall reactance?

Have you been yet introduced to phasor notation?

The answer to your question is "By Convention"
and it's related to the physical facts that
current leads voltage in capacitors
and
current lags voltage in inductors .

So a long long time ago the heavy thinkers {Steinmetz i think it was and Tesla picked right up on it)
decided that capacitance would get the minus sign and inductance the positive sign . Consistency kept their algebra simple. We never changed.

Be rigorous in your arithmetic and form good math habits. It'll pay off.

old jim
 
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