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The reactance of an inductor at $50 \mathrm{~Hz}$ is $10 \Omega$. The reactance of it at $200 \mathrm{~Hz}$ is
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Verified Answer
The correct answer is:
$20 \Omega$
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, $X=\omega L$
$$
=2 \pi f L
$$
$$
\begin{array}{rlrl}
\Rightarrow & & X & \propto f \\
\Rightarrow & & \frac{X_2}{X_1} & =\frac{f_2}{f_1}=\frac{200}{50}=4 \\
\Rightarrow & & X_2 & =4 X_1 \\
& & =4 \times 10=40 \Omega
\end{array}
$$
Initial reactance, $X_1=10 \Omega$
Final frequency, $f_2=200 \mathrm{~Hz}$
Final reactance, $X_2=$ ?
Since, reactance, $X=\omega L$
$$
=2 \pi f L
$$
$$
\begin{array}{rlrl}
\Rightarrow & & X & \propto f \\
\Rightarrow & & \frac{X_2}{X_1} & =\frac{f_2}{f_1}=\frac{200}{50}=4 \\
\Rightarrow & & X_2 & =4 X_1 \\
& & =4 \times 10=40 \Omega
\end{array}
$$
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