1. What is RLC Transient Response?

The RLC transient response describes how voltage or current changes over time in a circuit containing resistors (R), inductors (L), and capacitors (C) when the circuit is switched on or off. The equation \( v(t) = V (1 - e^{-t/\tau}) \) represents the charging curve of an RC circuit.

2. How Does the Calculator Work?

The calculator uses the transient response equation:

Where:

• \( v(t) \) — Voltage at time t (V)
• \( V \) — Source voltage (V)
• \( t \) — Time since switch (s)
• \( \tau \) — Time constant (s) = RC for RC circuits

Explanation: The equation shows how the voltage approaches the source voltage exponentially, with τ determining how quickly the circuit reaches steady state.

3. Importance of Transient Analysis

Details: Understanding transient response is crucial for designing circuits with specific timing characteristics, analyzing overshoot/undershoot, and ensuring proper circuit operation during switching events.

4. Using the Calculator

Tips: Enter source voltage in volts, time in seconds, and time constant in seconds. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What does the time constant τ represent?
A: The time constant is the time required for the voltage to reach ~63.2% of its final value (1-1/e).

Q2: How does this differ for RL circuits?
A: RL circuits follow the same exponential form but with τ = L/R. The current rather than voltage follows this curve.

Q3: What about underdamped RLC circuits?
A: Underdamped circuits exhibit oscillatory responses described by different equations involving natural frequency and damping ratio.

Q4: When is the circuit considered at steady state?
A: Typically after about 5τ, when the response has reached ~99.3% of final value.

Q5: How do I calculate τ for my circuit?
A: For RC circuits: τ = R×C. For RL circuits: τ = L/R. For parallel RLC, it's more complex.