Answer
(a) greater than
(b) $137Hz $
(c) $175\Omega $
Work Step by Step
(a) We know that $ X_C \gt X_L $
$\implies \frac{1}{\omega C}\gt \omega L $
This can be rearranged as
$\frac{1}{LC}\gt \omega^2$
$\implies \omega^2\lt \frac{1}{\sqrt{LC}}$
$\implies \omega^2\lt \omega_{\circ}$ Because $\omega_{\circ}=\frac{1}{\sqrt{LC}}$
$\implies \omega_{\circ}\gt \omega $
Thus, we conclude that the resultant frequency is greater than $60Hz $.
(b) We know that
$ f_{\circ}=\frac{1}{2\pi \sqrt{LC}}$
We plug in the known values to obtain:
$ f_{\circ}=\frac{1}{2\pi \sqrt{90\times 10^{-3}\times 15\times 10^{-6}}}$
$ f_{\circ}=137Hz $
(c) We know that the impedance of the circuit at resonance is $ Z=R $ and we are given that $ R=175\Omega $. Thus, impedance at resonance is $ Z=175\Omega $
