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Series RLC Circuit

An RLC circuit is an electrical circuit consisting of a resistor, an inductor and a capacitor, connected in series or in parallel.

The power factor decreases with the capacitance, frequency and electrical resistance. A lower magnetic inductance also decreases the power factor. The quality factor equals the resistance times the square root of the capacitance divided by the magnetic inductance. The tangent of the voltage\[Hyphen]current phase difference increases with the capacitance and frequency as well as with decreasing electrical resistance and decreasing magnetic inductance. The resonance angular frequency equals the reciprocal of the square root of the capacitance times the magnetic inductance.

Formula

{QuantityVariable["PF", "Unitless"] == QuantityVariable["R", "ElectricResistance"]/Sqrt[(-1/(2*Pi*QuantityVariable["C", "ElectricCapacitance"]*QuantityVariable["f", "Frequency"]) + 2*Pi*QuantityVariable["f", "Frequency"]*QuantityVariable["L", "MagneticInductance"])^2 + QuantityVariable["R", "ElectricResistance"]^2], Tan[QuantityVariable["ϕ", "Angle"]] == (-1/(2*Pi*QuantityVariable["C", "ElectricCapacitance"]*QuantityVariable["f", "Frequency"]) + 2*Pi*QuantityVariable["f", "Frequency"]*QuantityVariable["L", "MagneticInductance"])/QuantityVariable["R", "ElectricResistance"], QuantityVariable["Q", "Unitless"] == Sqrt[QuantityVariable["L", "MagneticInductance"]/QuantityVariable["C", "ElectricCapacitance"]]/QuantityVariable["R", "ElectricResistance"], QuantityVariable[Subscript["ω", "0"], "AngularFrequency"] == 1/Sqrt[QuantityVariable["C", "ElectricCapacitance"]*QuantityVariable["L", "MagneticInductance"]]}

symbol description physical quantity
PF power factor "Unitless"
R electric resistance "ElectricResistance"
C electric capacitance "ElectricCapacitance"
f frequency "Frequency"
L magnetic inductance "MagneticInductance"
ϕ voltage­current phase difference "Angle"
Q quality factor "Unitless"
ω0 resonance angular frequency "AngularFrequency"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Series RLC Circuit"]
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Get the formula:

In[2]:=
FormulaData[ResourceObject["Series RLC Circuit"]]
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Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Series RLC Circuit"], {QuantityVariable["PF","Unitless"] -> 0.003775`, QuantityVariable["\[Phi]","Angle"] -> Quantity[-89.78`, "AngularDegrees"], QuantityVariable["C","ElectricCapacitance"] -> Quantity[10, "Microfarads"]}]
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