Initial and Final Conditions
How to Use
- Select a preset (RC Charging, RC with Initial Charge, RL Energizing, or Thevenin-RC) using the buttons in the lower right.
- Click "Step Through Analysis" to advance through the five analysis stages:
- Step 1 — Original circuit with switch position shown
- Step 2 — t < 0 steady-state: capacitor → open circuit, inductor → short circuit
- Step 3 — t = 0⁺ continuity: stored-element values cannot jump
- Step 4 — t → ∞ steady-state: find final value
- Step 5 — Complete solution formula with calculated values, animated response curve
- Click "Reset" to return to Step 1 at any time.
Learning Objective
Students will solve for initial and final conditions given a circuit with a switch, then predict the transient response using the universal exponential formula:
\[x(t) = x(\infty) + [x(0^+) - x(\infty)]\,e^{-t/\tau}\]
Key Rules
| Element | t < 0 (before switch) | t = 0⁺ (just after) | t → ∞ (steady state) |
|---|---|---|---|
| Capacitor | Open circuit | V_C unchanged | Open circuit |
| Inductor | Short circuit | I_L unchanged | Short circuit |
The continuity conditions are the critical insight: capacitor voltage and inductor current cannot change instantaneously because that would require infinite power.