Inductive and capacitive reactance

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In summary, capacitive reactance is subtracted from inductive reactance when determining overall reactance because they are added in series and keep their respective signs. This convention was established due to the physical fact that current leads voltage in capacitors and lags in inductors. This decision was made long ago for consistency and simplicity in algebra. It is important to be diligent in arithmetic and form good math habits.
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fonz
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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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FAQ: Inductive and capacitive reactance

What is inductive reactance?

Inductive reactance is the opposition to the flow of alternating current (AC) caused by an inductor. It is measured in ohms and is directly proportional to the frequency of the AC and the inductance of the inductor.

What is capacitive reactance?

Capacitive reactance is the opposition to the flow of alternating current (AC) caused by a capacitor. It is measured in ohms and is inversely proportional to the frequency of the AC and the capacitance of the capacitor.

How do inductive and capacitive reactance affect AC circuits?

Inductive reactance causes an AC circuit to lag in phase, while capacitive reactance causes it to lead in phase. This can result in changes in the amplitude and phase of the AC signal in the circuit.

What is the difference between inductive and capacitive reactance?

The main difference between inductive and capacitive reactance is the type of component that causes the opposition to the flow of AC. Inductive reactance is caused by an inductor, while capacitive reactance is caused by a capacitor. They also have opposite effects on the phase of the AC signal in a circuit.

How can inductive and capacitive reactance be calculated?

Inductive reactance can be calculated using the formula XL = 2πfL, where XL is the inductive reactance in ohms, f is the frequency in hertz, and L is the inductance in henrys. Capacitive reactance can be calculated using the formula XC = 1/(2πfC), where XC is the capacitive reactance in ohms, f is the frequency in hertz, and C is the capacitance in farads.

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