Inductive Reactance

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A pure inductor of inductance 0.1 H is connected to an alternating source operating at an angular frequency of 100 rad/s. What is the inductive reactance offered to the current at this frequency?

RankGuru · Accepted Answer

Inductive reactance is the frequency-dependent opposition that an inductor presents to alternating current, arising because the back-EMF grows with how fast the current changes. It is given by $X_L = \omega L$, increasing linearly with angular frequency. Substituting $\omega = 100$ rad/s and $L = 0.1$ H gives $X_L = 100 \times 0.1 = 10\;\Omega$. The option 1 $\Omega$ wrongly divides instead of multiplies the inductance. The option 100 $\Omega$ ignores the inductance value entirely and quotes the frequency. The option 0.1 $\Omega$ reports the inductance itself with mismatched units. Unlike resistance, reactance dissipates no average power; it merely limits current magnitude while shifting its phase. This is the NCERT result that an inductor blocks high frequencies more strongly, behaving like an open circuit as $\omega \to \infty$. A dimensional check confirms (rad/s)(H) reduces to ohms, and the modest value is consistent with a small inductance at low frequency; doubling the frequency would double this reactance, as expected.

Inductive Reactance

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