RC/RL Time Constant & Transient Solver mechanism

Model scope

The time-constant formulas are conditionally correct, but the specification is incomplete and the single transient formula cannot support all claimed RC/RL voltage/current charge/discharge outputs. The instrument must define circuit type, response quantity, initial and final conditions, unit normalization, and valid input domains before it can be labeled honestly.

• τ=RC is correct for an ideal first-order RC circuit when R is the Thevenin/effective resistance seen by the capacitor and C is in farads.
• τ=L/R is correct for an ideal first-order RL circuit when R is the effective resistance seen by the inductor and L is in henries.
• v(t)=V(1−e^(−t/τ)) is the capacitor charging-voltage formula when V is the final capacitor voltage, t is nonnegative, and the capacitor starts uncharged.
• The stated formula does not provide the RC discharge formula v(t)=V0e^(−t/τ).
• The stated formula does not provide the RL current formula i(t)=(V/R)(1−e^(−t/τ)); using v(t)=V(1−e^(−t/τ)) for i(t) is dimensionally incorrect.
• The stated formula does not provide the RL inductor-voltage decay formula vL(t)=Ve^(−t/τ).

Units and conventions

• R must be expressed in ohms, C in farads, L in henries, V in volts, t in seconds, and τ is then in seconds.
• For RC charging, V is assumed to be the final applied/source voltage and the capacitor initially has 0 V.
• For RL current rise, V is assumed to be the applied DC source voltage, the inductor initially has zero current, and the final current is V/R.
• R must represent the total effective resistance relevant to the transient, including source and load resistance where applicable.
• Percent charged/current-rise percentage is dimensionless and equals 100 times the normalized transient response.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "circuit": "RC charge",
    "R": 1000,
    "R_unit": "ohm",
    "C": 0.000001,
    "C_unit": "F",
    "V": 5,
    "V_unit": "V",
    "t": 0.001,
    "t_unit": "s"
  },
  "expected_outputs": {
    "tau": 0.001,
    "tau_unit": "s",
    "v_t": 3.160602794,
    "v_t_unit": "V",
    "percent_charged": 63.21205588
  },
  "working": "τ=RC=1000×0.000001=0.001 s. t/τ=0.001/0.001=1. v(t)=5(1−e^(−1))=5(1−0.3678794412)=5×0.6321205588=3.160602794 V. Percent charged=100×0.6321205588=63.21205588%."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The solver has an undefined exact-input case at R = 0 because τ = RC = 0 and the exponential requires division by τ. It also lacks an explicit transient-mode or initial-condition input, so it cannot reliably distinguish charging from discharging behavior; signed-voltage convention is likewise unspecified.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche2/tranche2-results.json
• BOUNDARY_HAZARD_CATALOG.json