Capacitive reactance of a capacitor in an $\mathrm{AC}$ circuit is 6 $\mathrm{k} \Omega$. If the same…
Capacitive reactance of a capacitor in an $\mathrm{AC}$ circuit is 6 $\mathrm{k} \Omega$. If the same capacitor is connected to an $\mathrm{AC}$ source of double the frequency, the capacitive reactance will become
$6 \mathrm{k} \Omega$
$3 \mathrm{k} \Omega$
$1.5 \mathrm{k} \Omega$
$8.5 \mathrm{k} \Omega$
Solution
As we know
$\chi_{\mathrm{C}} \propto \frac{1}{\omega} \Rightarrow \frac{\chi_{\mathrm{C}_2}}{\chi_{\mathrm{C}_1}}=\frac{\omega_1}{\omega_2} \Rightarrow \chi_{\mathrm{C}_2}=6 \mathrm{k} \Omega \times \frac{\omega}{2 \omega}=3 \mathrm{k} \Omega$