Electricity & Magnetism
Impedance (RLC Series)
Total impedance of series RLC circuit.
Variables
ZΩ
Impedance
Total opposition to AC
In SI units: kg·m²/(A²·s³)
Allowed values: 0 or more
RΩ
Resistance
Resistance
In SI units: kg·m²/(A²·s³)
Allowed values: 0 or more
XLΩ
Inductive reactance
ωL
In SI units: kg·m²/(A²·s³)
Allowed values: greater than 0
XCΩ
Capacitive reactance
1/(ωC)
In SI units: kg·m²/(A²·s³)
Allowed values: greater than 0
Derivation
From phasor addition: V = √(V_R² + (V_L - V_C)²), Z = V/I.
Your notes
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Other electricity & magnetism formulas with the same quantities
- Ohm's Law (Electric Circuits) shares Resistance
- Electric Power (Electric Circuits) shares Resistance
- Resistance (Electric Circuits) shares Resistance
- RC Time Constant (Capacitance) shares Resistance
- RL Time Constant (Electromagnetic Induction) shares Resistance
Where this formula is listed
- Electricity & Magnetism formulas, under AC Circuits, alongside RMS Voltage/Current.
- In the electricity & magnetism list it comes after Inductive Reactance and before Resonant Frequency (LC).
- Electricity & Magnetism formula sheet, one of 48 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the Impedance (RLC Series) formula?
Impedance (RLC Series) is written Z = √(R² + (X_L − X_C)²). Total impedance of series RLC circuit. It belongs to Electricity & Magnetism, under AC Circuits.
What are the units in Z = √(R² + (X_L − X_C)²)?
In SI units, Z is impedance, measured in kg·m²/(A²·s³); R is resistance, measured in kg·m²/(A²·s³); X_L is inductive reactance, measured in kg·m²/(A²·s³); X_C is capacitive reactance, measured in kg·m²/(A²·s³).
How is the Impedance (RLC Series) formula derived?
From phasor addition: V = √(V_R² + (V_L - V_C)²), Z = V/I. The result is Z = √(R² + (X_L − X_C)²).