Question

At a certain frequency $\omega_{1}$, the reactance of a certain capacitor equals to that of a certain inductor. If the frequency is changed to $\omega_{2}=2 \omega_{1}$, the ratio of the reactance of the inductor to that of the capacitor is _______.

Answer 1

At a certain frequency $\omega_{1}, X_{L_{1}}=X_{C_{1}}, \omega_{1} L=\frac{1}{\omega_{1} C}$
Now, frequency is changed to
$X_{L_{2}}=\omega_{2} L=2 \omega_{1} L=2\left(\frac{1}{\omega_{1} C}\right)=2\left(\frac{2}{\omega_{2} C}\right)=4 \times C_{2}$
Ratio of reactance of inductor to capacitor, i.e.
$\frac{X_{L_{2}}}{X_{C_{2}}}=4$