Answer
(a) $494Hz$
(b) $180\Omega$
(c) $0.58$
Work Step by Step
(a) We know that
$f=\frac{1}{2\pi \sqrt{LC}}$
We plug in the known values to obtain:
$f=\frac{1}{2\pi \sqrt{(0.518)(0.200\times 10^{-6})}}$
$f=494Hz$
(b) We can find the impedance as
$Z=\sqrt{R^2+(\omega L-\frac{1}{\omega C})^2}$
We plug in the known values to obtain:
$Z=\sqrt{(105)^2+(2\pi(494.47)(0.518)-\frac{1}{2\pi(494.47)(0.220)})^2}=180\Omega$
(c) The power factor can be determined as
$cos\phi=\frac{R}{Z}$
We plug in the known values to obtain:
$cos\phi=\frac{105}{180}=0.58$
