Question 380: AC fundamentals

Question

The capacitive reactance of a capacitor '$$C$$' is $$\mathrm{X} \Omega$$. Both, the frequency of a.c. supply and capacitance of the above capacitor are doubled. The new capacitive reactance will be

Accepted Answer

Given, $$\mathrm{X}_{\mathrm{C}}=\mathrm{X} \Omega$$
$$\Rightarrow \frac{1}{2 \pi \mathrm{fC}}=\mathrm{X} \Omega$$
New Capacitance $$\mathrm{C}=2 \mathrm{C}$$ and new frequency $$\mathrm{f}^{\prime}=2 \mathrm{f}$$
$$	herefore \quad$$ New capacitive reactance
$$\mathrm{X}_{\mathrm{C}}^{\prime}=\frac{1}{2 \pi(2 \mathrm{f})(2 \mathrm{C})}$$
$$\begin{aligned}
& =\frac{1}{(2 \pi)(4 \mathrm{fC})} \
& =\frac{1}{4} X_C \
& =\frac{X}{4} \Omega
\end{aligned}$$

Answer

$$\frac{\mathrm{X}}{4} \Omega$$

Answer

$$\frac{\mathrm{X}}{2} \Omega$$

Answer

$$2 \mathrm{X} \Omega$$

Answer

$$4 \mathrm{X} \Omega$$

AC fundamentals

The capacitive reactance of a capacitor '$C' is \mathrm{X} \Omega$. Both, the frequency of a.c. supply and capacitance of the above capacitor are doubled. The new capacitive reactance will be

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