The reactance of an inductor at $50 \mathrm{~Hz}$ is $10 \Omega$. The reactance of it at $200 \mathrm{~Hz}$ is

The reactance of an inductor at $50 \mathrm{~Hz}$ is $10 \Omega$. The reactance of it at $200 \mathrm{~Hz}$ is
  1. $10 \Omega$
  2. $40 \Omega$
  3. $2.5 \Omega$
  4. $20 \Omega$

Solution

Given, initial frequency, $f_1=50 \mathrm{~Hz}$ Initial reactance, $X_1=10 \Omega$ Final frequency, $f_2=200 \mathrm{~Hz}$ Final reactance, $X_2=$ ? Since, reactance, $X=\omega L$ $ =2 \pi f L $ $ \begin{array}{rlrl} \Rightarrow & & X & \propto f \\ \Rightarrow & & \frac{X_2}{X_1} & =\frac{f_2}{f_1}=\frac{200}{50}=4 \\ \Rightarrow & & X_2 & =4 X_1 \\ & & =4 \times 10=40 \Omega \end{array} $

Asked in: AP EAMCET 2021 (23 Aug Shift 1)

Practice more AC Circuits questions on Aicharya