Series RLC Circuit Calculator
Enter R, L, C, and frequency to analyze your circuit.
What Is an RLC Circuit Calculator?
An RLC circuit calculator analyzes a circuit containing a resistor, inductor, and capacitor. In an AC circuit, these three components combine to determine total impedance, reactance, phase angle, and resonance behavior.
This calculator is designed for a series RLC circuit. Enter resistance, inductance, capacitance, and operating frequency to calculate the most important electrical values instantly.
Series RLC Circuit Formulas
A series RLC circuit uses separate equations for inductive reactance, capacitive reactance, total reactance, and impedance.
XC = 1 / (2πfC)
X = XL - XC
Z = √(R² + X²)
Resistance is measured in ohms, frequency in hertz, inductance in henries, and capacitance in farads. The calculated impedance is also measured in ohms.
How to Use the RLC Circuit Calculator
- Enter the resistance value and select its unit.
- Enter the circuit frequency in Hz, kHz, MHz, or GHz.
- Enter the inductance and select nH, µH, mH, or H.
- Enter the capacitance using pF, nF, µF, mF, or F.
- Click Calculate RLC Circuit.
- Review impedance, reactance, phase angle, resonance frequency, and quality factor.
The calculator automatically converts each input into the correct SI unit before performing the calculations.
RLC Circuit Calculation Example
Suppose a series circuit has 100 Ω resistance, 10 mH inductance, 10 µF capacitance, and operates at 1 kHz.
XL ≈ 62.83 Ω
XC = 1 / (2π × 1000 × 0.00001)
XC ≈ 15.92 Ω
X ≈ 46.92 Ω
Z ≈ 110.46 Ω
Because inductive reactance is greater than capacitive reactance, this example behaves as a net inductive circuit at 1 kHz.
RLC Resonance Frequency
Series resonance occurs when inductive reactance and capacitive reactance become equal. Their effects cancel, leaving resistance as the main contributor to impedance.
At the ideal resonance frequency, XL equals XC, the net reactance is zero, and the phase angle is approximately zero degrees.
Understanding RLC Circuit Behavior
Inductive Circuit
When XL is greater than XC, net reactance is positive and the circuit behaves inductively.
Capacitive Circuit
When XC is greater than XL, net reactance is negative and the circuit behaves capacitively.
Resonant Circuit
When XL and XC are equal, their reactances cancel and the series circuit behaves mainly resistively.
RLC Circuit Phase Angle
The phase angle indicates how voltage and current are positioned relative to each other in an AC circuit.
A positive angle represents a net inductive circuit, while a negative angle represents a net capacitive circuit. Near resonance, the phase angle approaches zero.
Quality Factor of a Series RLC Circuit
The quality factor, commonly represented by Q, describes how sharply a resonant RLC circuit responds around its resonant frequency.
or
Q = ω0L / R
A higher Q generally represents a narrower and more selective resonance response in an idealized series RLC circuit.
RLC Circuit Components Explained
Resistor
A resistor provides resistance and dissipates electrical energy. It helps control current and influences the circuit's quality factor.
Inductor
An inductor produces inductive reactance. Its opposition to AC increases as the operating frequency increases.
Capacitor
A capacitor produces capacitive reactance. Its reactance decreases as the operating frequency increases.
Common RLC Calculator Units
| Quantity | Common Units |
|---|---|
| Resistance | mΩ, Ω, kΩ, MΩ |
| Frequency | Hz, kHz, MHz, GHz |
| Inductance | nH, µH, mH, H |
| Capacitance | pF, nF, µF, mF, F |
| Reactance | Ω, kΩ, MΩ |
| Impedance | Ω, kΩ, MΩ |
| Phase Angle | Degrees (°) |
Frequently Asked Questions
What is an RLC circuit?
An RLC circuit contains a resistor, inductor, and capacitor. These components interact in an AC circuit to create resistance, inductive reactance, capacitive reactance, and resonance.
How do you calculate RLC impedance?
For a series RLC circuit, first calculate XL and XC. Then calculate net reactance X = XL − XC and use Z = √(R² + X²) to find the impedance magnitude.
What is resonance in an RLC circuit?
Resonance occurs when inductive reactance equals capacitive reactance. In an ideal series RLC circuit, the net reactance becomes zero at this frequency.
What is the RLC resonance frequency formula?
The ideal resonance frequency is fr = 1 / (2π√LC), where L is inductance in henries and C is capacitance in farads.
What does a positive RLC phase angle mean?
A positive phase angle indicates that the circuit has more inductive reactance than capacitive reactance at the selected frequency.
What does a negative phase angle mean?
A negative phase angle indicates that capacitive reactance is greater than inductive reactance, so the circuit is net capacitive.
What is the quality factor of an RLC circuit?
The quality factor describes the sharpness of resonance. For an ideal series RLC circuit it can be calculated using Q = (1/R)√(L/C).