AC Circuits Formulas
AC circuit formulas describe how voltage, current, and impedance interact in sinusoidal systems. These calculators handle reactance, phase, and resonance so you can analyse filters, tuned circuits, and power factor. They are the bridge between simple DC analysis and real-world signals.
AC Circuits Formula Calculators
- Resonant Frequency f = 1 / (2π√(LC)) Inductance 100 nH, Capacitance 1 pF → Frequency = 0.5033 GHz
- Impedance (RLC Series) Z = √(R² + (XL − XC)²) Resistance 1 Ω, Inductive Reactance 2.2 Ω, Capacitive Reactance 4.7 Ω → Z = 2.693 Ω
- Quality Factor (Bandwidth) Q = f₀ / BW Resonant Frequency 100 Hz, Bandwidth 5 Hz → Q Factor = 20
- Quality Factor (RLC) Q = (1/R) × √(L/C) Resistance 1 Ω, Inductance 100 nH, Capacitance 1 pF → Q = 316.2
- Power Factor PF = P / S = cos(φ) Real Power 10 mW, Apparent Power 22 mW → Power Factor = 0.4545
- Apparent Power S = √(P² + Q²) Real Power 22 mW, Reactive Power 47 mW → Apparent Power = 51.89 mW
- Reactive Power Q = S × sin(φ) Apparent Power 22 mW, Phase Angle 1.5 ° → Reactive Power = 0.5759 mW
- RLC Circuit Bandwidth BW = f0 / Q Resonant Frequency 100 Hz, Quality Factor 0.025 → Bandwidth = 4 kHz
- AC RMS / Peak Conversion V_rms = V_peak / √2 Peak Voltage 0.726 V → RMS Voltage = 0.5134 V
- Transformer Turns Ratio N = V1 / V2 Primary Voltage 0.33 V, Secondary Voltage 0.726 V → Turns Ratio = 0.4545
- Average Rectified Voltage V_avg = 0.637 × Vpeak Peak Voltage 0.726 V → Average Voltage = 0.4625 V
- Three-Phase Line vs Phase Voltage V_line = √3 × V_phase Phase Voltage 0.726 V → Line-to-Line Voltage = 1.257 V
- Power Factor Correction Capacitor C = Qc / (ω × V²) Reactive Power 0.025, Line Frequency 5 Hz, Line Voltage RMS 0.33 V → Capacitance = 7.307 mF
- Transformer Efficiency η = Pout / (Pout + Piron + Pcopper) Output Power 10 mW, Core (Iron) Loss 22 mW, Copper Loss 47 mW → η = 0.1266
- Inrush Current I_inrush = Vpeak / Zsource Peak Voltage 0.33 V, Source Impedance 1 Ω → Inrush Current = 0.33 A
- Complex Impedance Magnitude (RLC) |Z| = √(R² + (ωL − 1/(ωC))²) Resistance 2.2 Ω, Frequency 5 Hz, Inductance 100 µH, Capacitance 100 nF → Impedance Magnitude = 0.3183 MΩ
- AC Phase Angle φ = arctan((XL − XC) / R) Inductive Reactance 1 Ω, Capacitive Reactance 2.2 Ω, Resistance 4.7 Ω → φ = -14.32
- Power Triangle (S, P, Q) S² = P² + Q² Real Power (W) 10 mW, Reactive Power (VAR) 0.055 → Apparent Power (VA) = 0.0559
- Phasor Magnitude (Rect → Polar) |Z| = √(R² + X²) Real Part 2.2 Ω, Imaginary Part 4.7 Ω → Magnitude = 5.189 Ω
- Phasor Angle (Rect → Polar) θ = atan(X / R) Real Part 1 Ω, Imaginary Part 2.2 Ω → Phase Angle = 65.56 °
- Phasor Real Part (Polar → Rect) R = |Z| · cos(θ) Magnitude 2.2 Ω, Phase Angle 1.5 ° → Real Part = 2.199 Ω
- Phasor Imaginary Part (Polar → Rect) X = |Z| · sin(θ) Magnitude 2.2 Ω, Phase Angle 1.5 ° → Imaginary Part = 57.59 mΩ
- Parallel (Tank) Resonant Frequency f = (1/2π)·√(1/LC − R²/L²) Inductance 100 µH, Capacitance 100 pF, Coil Resistance 1 Ω → Resonant Frequency = 1.592 MHz
- Waveform Form Factor FF = Vrms / Vavg RMS Value 0.33 V, Average Value 0.726 V → Form Factor = 0.4545
- Peak-to-Peak Voltage Vpp = 2 · Vpeak Peak (Amplitude) 0.726 V → Peak-to-Peak = 1.452 V
- Instantaneous AC Voltage v = Vmax · sin(θ) Peak Voltage 0.726 V, Phase Angle 1.5 ° → Instantaneous Voltage = 19 mV
- Angular Frequency ω = 2π · f Frequency 5 Hz → Angular Frequency = 31.42 rad/s
Worked result for every AC Circuits formula
| Formula | Expression | Worked result |
|---|---|---|
| Resonant Frequency | f = 1 / (2π√(LC)) | Inductance 100 nH, Capacitance 1 pF → Frequency = 0.5033 GHz |
| Impedance (RLC Series) | Z = √(R² + (XL − XC)²) | Resistance 1 Ω, Inductive Reactance 2.2 Ω, Capacitive Reactance 4.7 Ω → Z = 2.693 Ω |
| Quality Factor (Bandwidth) | Q = f₀ / BW | Resonant Frequency 100 Hz, Bandwidth 5 Hz → Q Factor = 20 |
| Quality Factor (RLC) | Q = (1/R) × √(L/C) | Resistance 1 Ω, Inductance 100 nH, Capacitance 1 pF → Q = 316.2 |
| Power Factor | PF = P / S = cos(φ) | Real Power 10 mW, Apparent Power 22 mW → Power Factor = 0.4545 |
| Apparent Power | S = √(P² + Q²) | Real Power 22 mW, Reactive Power 47 mW → Apparent Power = 51.89 mW |
| Reactive Power | Q = S × sin(φ) | Apparent Power 22 mW, Phase Angle 1.5 ° → Reactive Power = 0.5759 mW |
| RLC Circuit Bandwidth | BW = f0 / Q | Resonant Frequency 100 Hz, Quality Factor 0.025 → Bandwidth = 4 kHz |
| AC RMS / Peak Conversion | V_rms = V_peak / √2 | Peak Voltage 0.726 V → RMS Voltage = 0.5134 V |
| Transformer Turns Ratio | N = V1 / V2 | Primary Voltage 0.33 V, Secondary Voltage 0.726 V → Turns Ratio = 0.4545 |
| Average Rectified Voltage | V_avg = 0.637 × Vpeak | Peak Voltage 0.726 V → Average Voltage = 0.4625 V |
| Three-Phase Line vs Phase Voltage | V_line = √3 × V_phase | Phase Voltage 0.726 V → Line-to-Line Voltage = 1.257 V |
| Power Factor Correction Capacitor | C = Qc / (ω × V²) | Reactive Power 0.025, Line Frequency 5 Hz, Line Voltage RMS 0.33 V → Capacitance = 7.307 mF |
| Transformer Efficiency | η = Pout / (Pout + Piron + Pcopper) | Output Power 10 mW, Core (Iron) Loss 22 mW, Copper Loss 47 mW → η = 0.1266 |
| Inrush Current | I_inrush = Vpeak / Zsource | Peak Voltage 0.33 V, Source Impedance 1 Ω → Inrush Current = 0.33 A |
| Complex Impedance Magnitude (RLC) | |Z| = √(R² + (ωL − 1/(ωC))²) | Resistance 2.2 Ω, Frequency 5 Hz, Inductance 100 µH, Capacitance 100 nF → Impedance Magnitude = 0.3183 MΩ |
| AC Phase Angle | φ = arctan((XL − XC) / R) | Inductive Reactance 1 Ω, Capacitive Reactance 2.2 Ω, Resistance 4.7 Ω → φ = -14.32 |
| Power Triangle (S, P, Q) | S² = P² + Q² | Real Power (W) 10 mW, Reactive Power (VAR) 0.055 → Apparent Power (VA) = 0.0559 |
| Phasor Magnitude (Rect → Polar) | |Z| = √(R² + X²) | Real Part 2.2 Ω, Imaginary Part 4.7 Ω → Magnitude = 5.189 Ω |
| Phasor Angle (Rect → Polar) | θ = atan(X / R) | Real Part 1 Ω, Imaginary Part 2.2 Ω → Phase Angle = 65.56 ° |
| Phasor Real Part (Polar → Rect) | R = |Z| · cos(θ) | Magnitude 2.2 Ω, Phase Angle 1.5 ° → Real Part = 2.199 Ω |
| Phasor Imaginary Part (Polar → Rect) | X = |Z| · sin(θ) | Magnitude 2.2 Ω, Phase Angle 1.5 ° → Imaginary Part = 57.59 mΩ |
| Parallel (Tank) Resonant Frequency | f = (1/2π)·√(1/LC − R²/L²) | Inductance 100 µH, Capacitance 100 pF, Coil Resistance 1 Ω → Resonant Frequency = 1.592 MHz |
| Waveform Form Factor | FF = Vrms / Vavg | RMS Value 0.33 V, Average Value 0.726 V → Form Factor = 0.4545 |
| Peak-to-Peak Voltage | Vpp = 2 · Vpeak | Peak (Amplitude) 0.726 V → Peak-to-Peak = 1.452 V |
| Instantaneous AC Voltage | v = Vmax · sin(θ) | Peak Voltage 0.726 V, Phase Angle 1.5 ° → Instantaneous Voltage = 19 mV |
| Angular Frequency | ω = 2π · f | Frequency 5 Hz → Angular Frequency = 31.42 rad/s |
Variables used across AC Circuits formulas
- f — Resonant frequency in hertz (Hz)
- L — Inductance in henries (H)
- C — Capacitance in farads (F)
- Z — Impedance magnitude in ohms (Ω)
- R — Resistance in ohms (Ω)
- XL — Inductive reactance in ohms (Ω)
- XC — Capacitive reactance in ohms (Ω)
- Q — Quality factor (dimensionless)
- f₀ — Resonant (center) frequency in hertz (Hz)
- BW — Bandwidth at -3dB points in hertz (Hz)
- PF — Power factor (0 to 1, dimensionless)
- P — Real (true) power in watts (W)
- S — Apparent power in volt-amperes (VA)
- φ — Phase angle between voltage and current (degrees)
- f0 — Resonant (center) frequency (Hz)
- V_rms — Root mean square voltage (V)
- V_peak — Peak (maximum) voltage (V)
- N — Turns ratio (primary to secondary, dimensionless)
- V1 — Primary (input) voltage (V)
- V2 — Secondary (output) voltage (V)
- V_avg — Average rectified voltage (V)
- V_line — Line-to-line (phase-to-phase) voltage (V)
- V_phase — Phase-to-neutral voltage (V)
- Qc — Reactive power to compensate (VAR)
- V — RMS line voltage (V)
- Pout — Output (load) power (W)
- P_iron — Core loss from hysteresis and eddy currents (W)
- P_copper — Winding I²R loss (W)
- I_inrush — Peak inrush current (A)
- Z_source — Total impedance including wiring, NTC, and source (Ω)
- |Z| — Impedance magnitude (Ω)
- X_L — Inductive reactance, ωL (Ω)
- X_C — Capacitive reactance, 1/(ωC) (Ω)
- X — Reactance / imaginary part (Ω)
- θ — Phase angle (degrees)
- FF — Form factor (dimensionless)
- Vrms — RMS value of the waveform (V)
- Vavg — Average (rectified mean) value (V)
- Vpp — Peak-to-peak voltage (V)
- Vpeak — Peak amplitude from zero (V)
- v — Instantaneous voltage (V)
- Vmax — Peak amplitude (V)
- ω — Angular frequency (rad/s)
Questions people ask about AC Circuits
- Formula of bandwidth in rlc circuit — RLC Circuit Bandwidth
- Circuit bandwidth of rlc circuit — RLC Circuit Bandwidth
- Conversion from rms power to peak power in ac — AC RMS / Peak Conversion
- Mv transformer efficiency 10mva 99.x? what is typical for x? .2 .3 ? — Transformer Efficiency
- What do i need to calculate inrush — Inrush Current
- Ac capacitive phase angle formula — AC Phase Angle
- Power triangle s p+q — Power Triangle (S, P, Q)
- Power triangle formula calculator — Power Triangle (S, P, Q)
- Ideal resonant tank — Parallel (Tank) Resonant Frequency
- Parallel resonance calculator — Parallel (Tank) Resonant Frequency
- If the rms voltage is e= 8sinwt + 6 sin 2wtwaht is the instantaneous voltage — Instantaneous AC Voltage
- Instantaneous value of phase a voltage — Instantaneous AC Voltage
Related Formula Categories
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