Question

The inductive reactance of a coil is $2500\Omega $. On increasing its self-inductance to three times, what will be the new inductive reactance?
(A) $7500\Omega $
(B) $2500\Omega $
(C) $1225\Omega $
(D) $zero$

Answer 1

Hint
 Use the formula for Inductive Reactance in an AC circuit as ${X_L} = 2\pi f.L$ where $f$ is the frequency of the AC electrical supply in hertz and $L$ is the inductance value of the coil in henry.

Complete step by step answer
We know that, the Inductive reactance is given by,
$ \Rightarrow {X_L} = 2\pi f.L$ … Equation 1, Where, $f$ is the frequency of the AC supply in hertz and L is the inductance of the coil in Henry.
Hence, then the new inductance be thrice the previous value, i.e.
$ \Rightarrow L' = 3L$
Then, the new inductive reactance will be as follows,
$ \Rightarrow X_L^1 = 2\pi f.L'$
Putting the value of $L'$ we get,
$ \Rightarrow X_L^1 = 2\pi f.3L = 3.2\pi f.L$
Now, substituting the value of $2\pi f.L$ from equation 1, we get,
$X_L^1 = 3{X_L}$
Also, we are given ${X_L} = 2500\Omega $ Therefore, we get,
$X_L^1 = 3 \times 2500 = 7500\Omega $.
Option (A) is correct.

Note
Alternative method, from equation 1, we can see that there is a linear relationship between Inductance and Inductive Reactance, so after establishing that, we can simply infer that an Inductor with 3 times inductance will have 3 times inductive reactance too. Therefore, New Inductive reactance will be three times of the old inductive reactance,
$ \Rightarrow X_L^1 = 3.{X_L} = 3 \times 2500 = 7500\Omega $
Which, is the correct option.