Question

Explain the term inductive reactance. State its unit and dimensions.

Answer 1

1. The opposing nature of an inductor to the flow of alternating current is called inductive reactance.
2. In an inductive circuit,
   i₀ = `"e"_0/(omega"L")` ….(1)
3. For a resistive ac circuit, according to Ohm’s law,
   i = `"V"/"R"` ….(2)
   where R = resistance in the circuit
4. Comparing equations (1) and (2), we can conclude that ωL plays a similar role in an inductive ac circuit as a resistor in a pure resistor circuit. 
5. Hence, the effective resistance X_L offered by the inductance L is called inductive reactance and is given as, 
   X_L = ωL = 2πfL.  .......….(∵ ω = 2π/T = 2πf)
   where f = frequency of the AC supply.
6. X_L is directly proportional to the inductance (L) and the frequency (f) of the alternating current.
7. In DC circuits, f = 0
   ∴ X_L = 0
   It implies that a pure inductor offers zero resistance to DC, i.e., it cannot reduce DC.  
   Thus, it passes DC and blocks AC of very high frequency.
8. In an inductive circuit, the self-induced emf opposes the growth as well as decay of current.
9. The dimensions of inductive reactance are [ML²T^-3I ^-2] and its SI unit is the ohm (Ω).