Alternating Current - Result Question 29

30. A capacitor has capacity $C$ and reactance $X$. If capacitance and frequency become double, then reactance will be

[2001]

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Answer:

Correct Answer: 30. (c)

Solution:

(c) Capacitive reactance, $X=\frac{1}{\omega C}=\frac{1}{2 \pi f C}$

$\Rightarrow X \propto \frac{1}{f C}$

$\therefore \frac{X^{\prime}}{X}=\frac{f}{f^{\prime}} \times \frac{C}{C^{\prime}}=\frac{f}{2 f} \times \frac{C}{2 C}=\frac{1}{4}$

$\Rightarrow X^{\prime}=\frac{X}{4}$

(d) Quality factor

$=\underline{\text{ Potential drop across capacitor or inductor }}$

Potential drop across R

$=\frac{I \omega L}{I R}=\frac{\omega L}{R}$