L=100µH, C=100pF → f₀≈1.5915 MHz f₀=1/(2π·√(L·C))=1/(2π·1e-7)≈1.5915 MHz。ω₀=2π·f₀≈10⁷ rad/s。特征阻抗 √(L/C)=√(1e-4/1e-10)=1000 Ω。{"result":"RLC resonant frequency (solve f0). L=100 µH (0.0001 H), C=100 pF (1e-10 F). f0 = 1/(2π·√(L·C)) = 1591549.431 Hz (1.5915 MHz). ω0 = 10000000 rad/s. Characteristic impedance √(L/C) = 1000 Ω.","metadata":{"input":{"solveFor":"frequency","L":100,"inductanceUnit":"µH","C":100,"capacitanceUnit":"pF","frequencyUnit":"MHz"},"result":{"solveFor":"frequency","inductance_H":0.0001,"inductance_uH":100,"capacitance_F":0.0000000001,"capacitance_pF":100,"frequency_Hz":1591549.431,"frequency_MHz":1.5915,"angularFrequency_rad_s":10000000,"characteristicImpedance_ohm":1000}}}
f=1 MHz, C=100pF → L≈253.30 µH L=1/((2π·f)²·C)=1/((2π·1e6)²·1e-10)≈2.533e-4 H=253.30 µH。特征阻抗 √(L/C)≈1591.55 Ω。{"result":"RLC resonant frequency (solve L). f0=1 MHz (1000000 Hz), C=100 pF (1e-10 F). L = 1/((2π·f)²·C) = 0.0002533 H (253.303 µH). ω0 = 6283185.3072 rad/s. Characteristic impedance √(L/C) = 1591.5494 Ω.","metadata":{"input":{"solveFor":"inductance","C":100,"capacitanceUnit":"pF","f":1,"frequencyUnit":"MHz"},"result":{"solveFor":"inductance","inductance_H":0.000253303,"inductance_uH":253.303,"capacitance_F":0.0000000001,"capacitance_pF":100,"frequency_Hz":1000000,"frequency_MHz":1,"angularFrequency_rad_s":6283185.3072,"characteristicImpedance_ohm":1591.5494}}}
f=1 MHz, L=253.30 µH → C=100 pF C=1/((2π·f)²·L)=1/((2π·1e6)²·2.533e-4)=1e-10 F=100 pF。验证:f₀=1/(2π·√(2.533e-4·1e-10))=1e6 Hz=1 MHz。特征阻抗 √(L/C)≈1591.55 Ω。{"result":"RLC resonant frequency (solve C). f0=1 MHz (1000000 Hz), L=253.3029591 µH (0.0002533 H). C = 1/((2π·f)²·L) = 0.0000000001 F (100 pF). ω0 = 6283185.3072 rad/s. Characteristic impedance √(L/C) = 1591.5494 Ω.","metadata":{"input":{"solveFor":"capacitance","L":253.3029591,"inductanceUnit":"µH","f":1,"frequencyUnit":"MHz"},"result":{"solveFor":"capacitance","inductance_H":0.0002533,"inductance_uH":253.303,"capacitance_F":0.0000000001,"capacitance_pF":100,"frequency_Hz":1000000,"frequency_MHz":1,"angularFrequency_rad_s":6283185.3072,"characteristicImpedance_ohm":1591.5494}}}