A series $$LCR$$ circuit fed with AC has resonant angular frequency $$\omega_0=2.0\times10^4\ \text{rad s}^{-1}$$. When the same circuit is driven at an angular frequency of $$2.5\times10^4\ \text{rad s}^{-1}$$, it has an impedance of $$1.0\ \text{k}\Omega$$ and phase constant of $$\phi=45^\circ$$. The values of $$L$$, $$C$$ and $$R$$ for this circuit may be

A

$$R=707\ \Omega$$

B

$$L=78.6\ \text{mH}$$

C

$$C=31.8\ \text{nF}$$

D

$$R=506\ \Omega$$