Inductive Reactance Formula

An inductor is a coil of wire that produces an electrical field when a current passes through it. Inductive Reactance is the measure of an inductor’s resistance to the alternating current. The concept of inductive reactance is similar to the resistance, except it always has a phase shift between voltage and current and emits no power. Its standard unit of measurement is ohms (Ω). It is represented by the symbol X_L and its dimensional formula is given by [M¹L²T^-3I^-2]. Its mathematical formula is equal to twice the product of pi, frequency and the inductance of an inductor.

Formula

X_L = 2πfL

where,

X_L is the inductive reactance,

π is a constant with the value of 3.14,

f is the frequency,

L is the inductance.

Sample Problems

Problem 1. Find the inductive reactance if the inductance is 5 H for a frequency of 20 Hz.

Solution:

We have,

f = 20

L = 5

Using the formula we have,

X_L = 2πfL

= 2 × 3.14 × 20 × 5

= 628.32 Ω

Problem 2. Find the inductive reactance if the inductance is 4 H for a frequency of 50 Hz.

Solution:

We have,

f = 50

L = 4

Using the formula we have,

X_L = 2πfL

= 2 × 3.14 × 50 × 4

= 1256.64 Ω

Problem 3. Find the inductive reactance if the inductance is 0.5 H for a time of 10 s.

Solution:

We have,

t = 10

L = 0.5

Using the formula f = 1/t we get,

f = 1/10

= 0.1 Hz

Using the formula we have,

X_L = 2πfL

= (2 × 3.14 × 0.1 × 0.5)

= 0.314 Ω

Problem 4. Find the inductive reactance if the inductance is 2.5 H for a time of 16 s.

Solution:

We have,

t = 16

L = 2.5

Using the formula f = 1/t we get,

f = 1/16

= 0.0625 Hz

Using the formula we have,

X_L = 2πfL

= 2 × 3.14 × 0.0625 × 2.5

= 0.98125 Ω

Problem 5. Find the inductance, if the inductive reactance is 2 Ω for a frequency of 25 Hz.

Solution:

We have,

X_L = 2

f = 25

Using the formula we have,

X_L = 2πfL

=> L = X_L/2πf

=> L = 2/(2 × 3.14 × 25)

=> L = 2/157

=> L = 0.012 H

Problem 6. Find the inductance, if the inductive reactance is 0.5 Ω for a frequency of 12 Hz.

Solution:

We have,

X_L = 0.5

f = 12

Using the formula we have,

X_L = 2πfL

=> L = X_L/2πf

=> L = 0.5/(2 × 3.14 × 12)

=> L = 0.5/75.36

=> L = 0.01 H

Problem 7. Find the frequency if inductive reactance is 4 Ω for the inductance of 2 H.

Solution:

We have,

X_L = 4

L = 2

Using the formula we have,

X_L = 2πfL

=> f = X_L/2πL

=> f = 4/(2 × 3.14 × 2)

=> f = 4/12.56

=> f = 0.32 Hz