Question

The reactance of a capacitor is $100\Omega$, when it is connected to a $100\text{Hz}$ AC supply. What will be its reactance, when it is connected to a $50\text{Hz}$ AC supply?

• A. $200\Omega$
• B. $100\Omega$
• C. $300\Omega$
• D. $400\Omega$

Answer 1

The correct option is A $200\Omega$

The capacitive reactance is given by,

$X_C=\frac{1}{\omega C}=\frac{1}{2\pi fC}$

$\Rightarrow \frac{(X_C{)}_1}{(X_C{)}_2}=\frac{f_2}{f_1}$

$\Rightarrow \frac{100}{(X_C{)}_2}=\frac{50}{100}$

$\Rightarrow (X_C{)}_2=200\Omega$

Hence, option $\left(A\right)$ is the correct answer.