Abstract: For a RL—C parallel resonant circuit，the relation between the maximum impedance value |Z|max and the impedance of resonant Z0 is presented strictly.The discrimination method of Z0 to be an extreme value is proposed and proved.The relative error of Z0 to |Z|max is analyzed，the relative error decreases as the circuit quality factor increases.If the Q is large enough，the difference of Z0 and |Z|max should be negligible，in this case the cireuit resonant impedance Z0=L/RC arrives at the maximum value.

Key words: resonant circuit, impedance, extreme value