At a frequency v$1$ the reactance of a certain capacitor equals that of a certain inductor. $($a$)$ If the frequency is changed to v$2=2$v$1,$ what is the ratio of the reactance of the inductor to that of the capacitor? Which reactance is larger? $($b$)$ If the frequency is changed to v$3=$ v$1>3,$ what is the ratio of the reactance of the inductor to that of the capacitor? Which reactance is larger? $($c$)$ If the capacitor and inductor are placed in series with a resistor of resistance R to form an L$-$R$-$C series circuit, what will be the resonance angular frequency of the circuit?