A resistor and a capacitor are connected in series with a variable inductor. When the circuit is connected to a $20V, 50H_Z$ supply, the maximum current obtained by varying the inductance is 2A. The voltage across the capacitor is 500V. Calculate the resistance, inductance and capacitance of the circuit.
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$V=230V \\ f_0=50H_Z \\ I_0=2A \\ V_{C0}=500V \\ \text{Resistance:} \\ R = \dfrac{V}{I_0} = \dfrac{230}{2}=115Ω \\ \text{Capacitance:} \\ X_{C0}= \dfrac{V_{CO}}{I_0} = \dfrac{500}{2} \\ X_{C0}= \dfrac{1}{2πf_0 C} \\ 250 = \dfrac{1}{2π×50×C} \\ \boxed{C=12.73μF} \\ \text{Inductance:} \\ \text{At resonance,} \\ X_{CO}= X_{LO}=250Ω \\ X_{LO}=2πf_0 L \\ 250=2π×50×L \\ \boxed{L=0.795 H}$