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Parallel Resistor-Inductor Capacitor Circuit

A parallel RLC circuit is an electrical circuit consisting of a resistor, an inductor and a capacitor, connected 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, frequency, 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"] == 1/(Sqrt[(2*Pi*QuantityVariable["C", "ElectricCapacitance"]*QuantityVariable["f", "Frequency"] - 1/(2*Pi*QuantityVariable["f", "Frequency"]*QuantityVariable["L", "MagneticInductance"]))^2 + QuantityVariable["R", "ElectricResistance"]^(-2)]*QuantityVariable["R", "ElectricResistance"]), Tan[QuantityVariable["ϕ", "Angle"]] == (2*Pi*QuantityVariable["C", "ElectricCapacitance"]*QuantityVariable["f", "Frequency"] - 1/(2*Pi*QuantityVariable["f", "Frequency"]*QuantityVariable["L", "MagneticInductance"]))*QuantityVariable["R", "ElectricResistance"], QuantityVariable["Q", "Unitless"] == Sqrt[QuantityVariable["C", "ElectricCapacitance"]/QuantityVariable["L", "MagneticInductance"]]*QuantityVariable["R", "ElectricResistance"], QuantityVariable[Subscript["ω", "0"], "AngularFrequency"] == 1/Sqrt[QuantityVariable["C", "ElectricCapacitance"]*QuantityVariable["L", "MagneticInductance"]]}

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

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Parallel Resistor-Inductor Capacitor Circuit"]
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Get the formula:

In[2]:=
FormulaData[ ResourceObject["Parallel Resistor-Inductor Capacitor Circuit"]]
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Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Parallel Resistor-Inductor Capacitor Circuit"], {QuantityVariable[ "PF","Unitless"] -> 0.353196`, QuantityVariable["L","MagneticInductance"] -> Quantity[1, "Millihenries"]}]
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