The unit of reactance is: [PMT/NEET-2003]
a. Ohm
b. Volt
c. Mho
d. Newton

Answer

The correct answer is: a. Ohm

Explanation

Reactance is the opposition offered by an inductor or capacitor to the flow of alternating current (AC).

• Just like resistance in DC circuits, reactance also limits current but in AC circuits, and it depends on frequency.
• Inductive reactance is given by:
  $ X_L = \omega L = 2\pi fL $
• Capacitive reactance is given by:
  $ X_C = \frac{1}{\omega C} = \frac{1}{2\pi fC} $

In both cases, the dimension of reactance is the same as resistance.

$
\text{Unit of reactance} = \frac{\text{Volt}}{\text{Ampere}} = \text{Ohm} \ (\Omega)
$

Why not the other options?

• Volt: Unit of potential difference, not opposition to current.
• Mho: Unit of conductance (reciprocal of resistance).
• Newton: Unit of force, unrelated to electric circuits.

Thus, reactance is expressed in ohms (Ω).

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How inductive reactance has a unit equal to volt/ampere

For $X_L = \omega L$:
$
[\omega] = s^{-1}, \quad [L] = \frac{V \cdot s}{A}
$
So,
$
[X_L] = s^{-1} \times \frac{V \cdot s}{A} = \frac{V}{A} = \Omega
$

Hence, $X_L$ has unit volt/ampere (ohm).

---

How capacitive reactance has a unit equal to volt/ampere

For capacitive reactance

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

• $[\omega] = s^{-1}$
• $[C] = \text{Farad} = \frac{Coulomb}{Volt} = \frac{A \cdot s}{V}$

So,
$
[\omega C] = s^{-1} \times \frac{A \cdot s}{V} = \frac{A}{V}
$

Hence,
$
[X_C] = \frac{1}{\omega C} = \frac{V}{A} = \Omega
$

Thus, capacitive reactance also has the unit volt/ampere (ohm).