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This is a trivial question in first year but, unfortunately, this popped up in an elementary yet compulsory lab experiment.

The capacitive reactance is defined as $$X_{c}=\frac{1}{\omega c}$$ The text I relied on in my first year stated this as the definition.

However, I've came across sources defining the capacitive reactance as $$X_{c}=\frac{1}{i \omega c}$$

I'm pretty sure both definition are valid and perhaps the latter being more general than the former definition. Could someone be kind enough to fill me in on a little bit more?

Qmechanic
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Physkid
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1 Answers1

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To this EE's eyes, both formulas are incorrect; the reactance of a capacitor is

$$X_C = -\frac{1}{\omega C} $$

and so the sign is incorrect in the first formula. Since reactance is the imaginary part of impedance

$$Z = R + iX$$

reactance is a real number and so the second formula can't be correct. It is instead the formula for the impedance of a capacitor

The impedance of a capacitor is

$$Z_C = 0 + iX_C = -i\frac{1}{\omega C} = \frac{1}{i\omega C}$$

Alfred Centauri
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