Question 350: AC fundamentals

Question

At a particular angular frequency, the reactance of capacitor and that of inductor is same. If the angular frequency is doubled, the ratio of the reactance of the capacitor to that of the inductor will be

Accepted Answer

At particular angular frequency $$\omega_0, X_L=1 / X_C$$
$$\Rightarrow \quad \omega_0 L=\frac{1}{\omega_c} \Rightarrow \omega_0=\frac{1}{\sqrt{L C}}$$
when $$\omega_0^{\prime}=2 \omega_0$$
$$\begin{aligned}
	herefore \quad \frac{X_C^{\prime}}{X_L^{\prime}} & =\frac{1}{\frac{\omega_0^{\prime} C}{\omega_0^{\prime} L}}=\frac{1}{\left(\omega_0^{\prime}ight)^2 L C} \
& =\frac{1}{\left(2 \omega_0ight)^2 L C}=\frac{1}{4 \omega_0^2 L C}=\frac{1}{4 \cdot \frac{1}{L C} 	imes L C}=\frac{1}{4}
\end{aligned}$$

Answer

1/4

Answer

1/2

Answer

2

Answer

4

AC fundamentals

At a particular angular frequency, the reactance of capacitor and that of inductor is same. If the angular frequency is doubled, the ratio of the reactance of the capacitor to that of the inductor will be

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