Enter Circuit Values
Use RMS voltage for power calculations. The model assumes ideal series parts.
Formula Used
The calculator uses standard ideal series RLC relationships.
| Quantity | Formula | Meaning |
|---|---|---|
| Angular frequency | ω = 2πf |
Converts frequency into radians per second. |
| Inductive reactance | XL = ωL |
Opposition caused by inductance. |
| Capacitive reactance | XC = 1 / (ωC) |
Opposition caused by capacitance. |
| Net reactance | X = XL - XC |
Positive means inductive. Negative means capacitive. |
| Impedance | |Z| = √(R² + X²) |
Total opposition to AC current. |
| Current | I = V / |Z| |
RMS current through the series path. |
| Resonance | f0 = 1 / (2π√LC) |
Frequency where XL and XC are equal. |
| Quality factor | Q = ω0L / R |
Shows resonance sharpness. |
| Bandwidth | BW = R / (2πL) |
Difference between half-power frequencies. |
How to Use This Calculator
- Enter the resistance value and choose its unit.
- Enter the inductance value and choose microhenry, millihenry, or henry.
- Enter the capacitance value and choose the required unit.
- Enter the operating frequency of the AC source.
- Enter the RMS source voltage.
- Press the calculate button.
- Review impedance, current, phase, power, resonance, bandwidth, and graph values.
- Use the CSV or PDF button to save the report.
Example Data Table
| Case | R | L | C | Frequency | Voltage | Expected Behavior |
|---|---|---|---|---|---|---|
| Audio filter check | 100 Ω | 10 mH | 10 µF | 1 kHz | 12 V | Near practical signal testing range. |
| Sharper tuned load | 25 Ω | 22 mH | 1 µF | 1.07 kHz | 5 V | Higher current near resonance. |
| Damped response | 500 Ω | 10 mH | 10 µF | 1 kHz | 12 V | Lower current and wider damping. |
Understanding a Series RLC Circuit
Core Idea
A series RLC circuit places resistance, inductance, and capacitance in one current path. The same current flows through every part. The voltage divides across each element. This simple layout creates rich behavior. It can filter signals, tune radios, shape pulses, and test power networks.
Reactance and Frequency
Resistance limits current and converts energy into heat. Inductance stores energy in a magnetic field. Capacitance stores energy in an electric field. These two storage effects oppose each other. Inductive reactance rises as frequency rises. Capacitive reactance falls as frequency rises. Their difference decides the net reactance.
Resonance Point
At resonance, inductive reactance equals capacitive reactance. The net reactance becomes zero. The impedance is then mostly resistance. Current reaches its highest safe value for the entered voltage. The phase angle moves close to zero degrees. This means voltage and current are nearly aligned.
Power and Phase
Away from resonance, the circuit acts differently. Below resonance, capacitive behavior usually leads. Above resonance, inductive behavior usually dominates. The calculator shows this shift using impedance, phase, reactance, and current. It also estimates real power, reactive power, apparent power, and power factor.
Quality and Bandwidth
Advanced users can inspect quality factor and bandwidth. A higher quality factor means a sharper resonance peak. A lower bandwidth means the circuit responds strongly near one frequency. This matters in filters and tuned loads. It also matters when voltage rise across the inductor or capacitor may exceed the source voltage.
Graph Review
The graph helps you see frequency response fast. It plots current and impedance across a wide range around resonance. This makes component changes easier to understand. Try changing capacitance or inductance first. Then adjust resistance to see damping and bandwidth effects.
Practical Safety
Use calculated values as design guidance. Real parts include tolerance, heat limits, core losses, dielectric losses, and stray wiring effects. Always check part ratings before building hardware. For high voltage or mains work, follow electrical standards and use qualified supervision.
Export and Compare
For documentation, export the computed table after each run. Keep a record of assumed frequency, voltage, and component units. This helps compare prototypes and lab readings later. When results look unusual, confirm units first. Millihenries, microfarads, and kilohms can change answers by large factors. Small errors create very different circuit behavior.
FAQs
1. What is a series RLC circuit?
A series RLC circuit connects a resistor, inductor, and capacitor in one path. The same current flows through all three components. The total voltage splits across resistance, inductance, and capacitance depending on frequency and impedance.
2. What does resonance mean?
Resonance occurs when inductive reactance equals capacitive reactance. Net reactance becomes zero. The circuit impedance is then mainly resistance. In an ideal series circuit, current becomes highest at this frequency.
3. Why can inductor voltage exceed source voltage?
Near resonance, the inductor and capacitor can exchange stored energy strongly. Their individual voltage drops may become larger than the source voltage. They still oppose each other, so the net reactive voltage can remain small.
4. What is quality factor?
Quality factor shows how sharp the resonance response is. A higher value means stronger selectivity and a narrower bandwidth. A lower value means more damping and a broader frequency response.
5. What is bandwidth in a series RLC circuit?
Bandwidth is the range between the lower and upper half-power frequencies. For an ideal series RLC circuit, it equals resistance divided by two pi times inductance. Larger resistance increases bandwidth.
6. Does this calculator use RMS values?
Yes. The source voltage input is treated as RMS voltage. This makes current, real power, reactive power, and apparent power suitable for standard AC circuit calculations.
7. Why does phase become negative or positive?
Phase depends on net reactance. If inductive reactance is greater, current lags voltage. If capacitive reactance is greater, current leads voltage. At resonance, phase is close to zero.
8. Are real parts exactly like these results?
No. Real components have tolerance, heat limits, parasitic resistance, leakage, and frequency losses. Use these results for design guidance. Verify final circuits with rated parts, measurements, and safe electrical practice.