Calculation
I = U / √[R² + (2πfL − 1/(2πfC))²]
Inductive and capacitive reactance have opposite signs; at resonance R limits current.
Busch 2006, Abschnitt 5.8.1
RLC series-circuit current
Inductive and capacitive reactance have opposite signs; at resonance R limits current.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- RMS current I — RMS value of the common current through R, L and C in sinusoidal steady state.
- RMS voltage U — RMS sinusoidal voltage across the complete series circuit.
- Resistance R — Total series resistance including winding and lead resistance.
- Inductance L — Effective coil inductance at the entered frequency and operating level.
- Capacitance C — Effective series capacitance at the entered frequency, not its tolerance limit.
- Frequency f — Frequency of the sinusoidal source; commonly 50 Hz or 60 Hz for mains.
Example
U=230 V, R=20 Ω, L=100 mH, C=100 µF and f=50 Hz give |Z|≈20.00 Ω and I≈11.50 A.
Assumptions and limits
Linear ideal components in sinusoidal steady state; switching transient, saturation, ESR frequency response and component ratings are excluded.
Understand RLC series-circuit current
This calculator combines resistor, inductor and capacitor in one AC calculation and shows directly how frequency and resonance change their common RMS current.
What does this quantity describe?
Series complex impedances add. The real part is R and the reactive part X=2πfL−1/(2πfC). Current uses |Z|=√(R²+X²). Below resonance X is capacitive; above it X is inductive.
Formula and variables
I = U / √[R² + (2πfL − 1/(2πfC))²]
X = 2πfL − 1/(2πfC)|Z| = √(R² + X²)I = U/|Z|
| Symbol / input | Meaning |
|---|---|
| RMS current I | RMS value of the common current through R, L and C in sinusoidal steady state. |
| RMS voltage U | RMS sinusoidal voltage across the complete series circuit. |
| Resistance R | Total series resistance including winding and lead resistance. |
| Inductance L | Effective coil inductance at the entered frequency and operating level. |
| Capacitance C | Effective series capacitance at the entered frequency, not its tolerance limit. |
| Frequency f | Frequency of the sinusoidal source; commonly 50 Hz or 60 Hz for mains. |
Choose the inputs correctly
U and I are RMS values. R includes all series resistance, not merely a separate resistor. L and C must be effective values at the frequency f supplied by the source.
How to use the calculator
Enter actual RMS voltage, frequency, R, L and C. Compare I with every component's current and loss ratings, especially near resonance.
Worked example
At 230 V, 20 Ω, 100 mH, 100 µF and 50 Hz, XL≈31.42 Ω and |XC|≈31.83 Ω nearly cancel. |Z|≈20.00 Ω and I≈11.50 A.
Understand the result and units
High current near resonance does not mean zero component voltage: individual inductor and capacitor voltages can greatly exceed supply voltage.
Use V, A, Ω, H/mH/µH, F/mF/µF/nF/pF and Hz/kHz. Prefixes are converted to coherent SI before calculation.
Typical applications
Teaching phasors and resonance, preliminary filter checks, and current estimates in sinusoidally supplied series networks.
Assumptions, limits and common mistakes
Sinusoidal steady state with linear idealised components only. Saturation, core loss, capacitor ESR/ESL, temperature, tolerances, transients and voltage ratings are excluded.
Common mistake: Do not add reactance magnitudes: XL and XC have opposite signs. Do not mix peak and RMS quantities.
Frequently asked questions
What is “RLC series-circuit current” used for?
Teaching phasors and resonance, preliminary filter checks, and current estimates in sinusoidally supplied series networks.
Where do the input values come from?
U and I are RMS values. R includes all series resistance, not merely a separate resistor. L and C must be effective values at the frequency f supplied by the source.
What does the result not cover?
Sinusoidal steady state with linear idealised components only. Saturation, core loss, capacitor ESR/ESL, temperature, tolerances, transients and voltage ratings are excluded.