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In a capactive circuit, the reactance of capacitor at frequency 'f' is ' $\mathrm{X}_{\mathrm{c}}{ }^{\prime}$. What will be
its reactance at frequency $4 \mathrm{f} ?$
Options:
its reactance at frequency $4 \mathrm{f} ?$
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Verified Answer
The correct answer is:
$\frac{X_{C}}{4}$
Capacitive reactance $\mathrm{X}_{\mathrm{c}}=\frac{1}{2 \pi \mathrm{fC}}$
$\begin{array}{l}
\therefore \frac{\mathrm{X}_{\mathrm{C}}^{\prime}}{\mathrm{X}_{\mathrm{c}}}=\frac{\mathrm{f}}{\mathrm{f}^{\prime}}=\frac{1}{4} \\
\therefore \mathrm{X}_{\mathrm{c}}^{\prime}=\frac{\mathrm{X}_{\mathrm{c}}}{4}
\end{array}$
$\begin{array}{l}
\therefore \frac{\mathrm{X}_{\mathrm{C}}^{\prime}}{\mathrm{X}_{\mathrm{c}}}=\frac{\mathrm{f}}{\mathrm{f}^{\prime}}=\frac{1}{4} \\
\therefore \mathrm{X}_{\mathrm{c}}^{\prime}=\frac{\mathrm{X}_{\mathrm{c}}}{4}
\end{array}$
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