Inductive Reactance
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?
Select the correct option:
Solution
10 \(\Omega\)
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.
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About This Question
- Subject
- physics
- Chapter
- electromagnetic induction and alternating currents
- Topic
- inductive reactance
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
10 \(\Omega\)
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.
This easy difficulty physics question is from the chapter electromagnetic induction and alternating currents, covering the topic of inductive reactance. It appeared in the 2025 exam.
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