Answer
The inductor and the capacitor have the same reactance when the frequency is $~~650~Hz$, which is the same frequency as the natural frequency of
an oscillating circuit with the same L and C.
Work Step by Step
In part (a), we found that the inductor and the capacitor have the same reactance when the frequency is $~~650~Hz$
We can find $\omega$ in an oscillating circuit with the same L and C:
$\omega = \frac{1}{\sqrt{L~C}}$
$\omega = \frac{1}{\sqrt{(6.0\times 10^{-3}~H)(10\times 10^{-6}~F)}}$
$\omega = 4082.5~rad/s$
We can find the frequency:
$f = \frac{\omega}{2\pi} = \frac{4082.5~rad/s}{2\pi} = 650~Hz$
The inductor and the capacitor have the same reactance when the frequency is $~~650~Hz$, which is the same frequency as the natural frequency of
an oscillating circuit with the same L and C.
