How does the RC Time Constant solver work?

The solver uses the fundamental RC circuit equations: τ = R × C, Vc(t) = Vs(1 - e^(-t/τ)), and fc = 1/(2πRC). By providing any two independent variables, the solver algebraically determines the remaining parameters.

What is the significance of the 5τ rule?

After 5 time constants (5τ), the capacitor voltage reaches 99.3% of the supply voltage, which is considered fully charged for most practical purposes. The charging curve is asymptotic, meaning it never quite reaches 100% theoretically.

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ElectronicsRC SolverTime-Domain

RC Time Constant & Charging Matrix

A universal RC circuit solver that resolves resistance, capacitance, time constant, cutoff frequency, and charging behavior from any two known electrical variables, with time-domain analysis and live charging curve visualization.

Known Variables Setup

Select 2 Known Variables

Resistance (R)

Circuit resistance

Capacitance (C)

Circuit capacitance

Voltage (V)

Supply voltage

Current (initial) (I₀)

Initial charging current

RC Charging Circuit

Waiting for valid inputs

Matrix Outputs

Invalid Inputs

Resistance (R)

—Ω

Capacitance (C)

—F

Time Constant (τ)

—

Cutoff Freq (f_c)

—Hz

Charging Curve

Vc(t)

Supply

Time-Domain Analysis

Voltage and current at a specific time during charging.

Target Time (t)

Time after switching

Vc(t)

—

I(t)

—

RC Time Constants

τ	Time	Vc	% Charge
Enter valid R, C, and V to see time constants

01 / Time Constant

RC Time Constant & Transient Response

The RC time constant (τ = R × C) defines how quickly a capacitor charges or discharges through a resistor. After one time constant, the capacitor reaches approximately 63.2% of its final voltage.

Engineering note

After 5 time constants (5τ), the capacitor is considered fully charged (>99.3%). The time constant is independent of the supply voltage.

02 / Filter Applications

RC Cutoff Frequency

The cutoff frequency (f_c = 1/(2πRC)) defines the -3dB point for RC low-pass and high-pass filters. Frequencies beyond this point are attenuated.

Filter Note

For low-pass filters, frequencies below f_c pass with minimal attenuation. For high-pass filters, frequencies above f_c pass through.

03 / Energy Storage

Capacitor Energy

The energy stored in a capacitor (E = ½CV²) is proportional to both capacitance and the square of the voltage. This energy can be released quickly, making capacitors useful for power delivery.

Energy note

Stored energy increases quadratically with voltage. For high-voltage applications, careful attention to capacitor voltage ratings is essential.

04 / Mathematical Roots

Algorithm & Core Equations

The solver derives the remaining RC circuit parameters from any two independent known values.

Governing Formula

tau = R times C

τSeconds

Time Constant

ROhms

Resistance

CFarads

Capacitance

Governing Formula

V_c(t) = V_s(1 - e^{-t/tau})

V_cVolts

Capacitor Voltage

V_sVolts

Supply Voltage

tSeconds

Time

τSeconds

Time Constant

TypeScript — RC Circuit Solver

type KnownCombo = 'RC' | 'RV' | 'RI' | 'CV' | 'CI' | 'VI';

function solveRCMatrix(
  known: KnownCombo,
  val1: number,
  val2: number
) {
  let R = NaN;
  let C = NaN;
  let V = NaN;
  let I = NaN;
  let tau = NaN;

  switch (known) {
    case 'RC':
      R = val1;
      C = val2;
      tau = R * C;
      break;

    case 'RV':
      R = val1;
      V = val2;
      I = V / R;
      break;

    case 'RI':
      R = val1;
      I = val2;
      V = I * R;
      break;

    case 'CV':
      C = val1;
      V = val2;
      break;

    case 'CI':
      C = val1;
      I = val2;
      break;

    case 'VI':
      V = val1;
      I = val2;
      R = V / I;
      break;
  }

  return { R, C, V, I, tau };
}

Engineering Scope & Limitations

Ideal Components

The solver assumes ideal resistors and capacitors without parasitic effects or tolerances.

Initial Conditions

All calculations assume the capacitor is initially discharged (Vc(0) = 0).

Linear Operation

The model assumes linear operation of the circuit, which is valid for most passive RC networks.