Question 1

How do you calculate the time constant τ of an RC circuit?

Accepted Answer

The time constant of an RC series circuit is τ = R × C (seconds). For example, with R = 1 kΩ and C = 10 μF, τ = 1000 × 10×10⁻⁶ = 0.01 s (10 ms). Under a step input, the capacitor voltage reaches approximately 63.2% of the final value at t = τ, and 99.3% at t = 5τ. The value 5τ is called the settling time.

Question 2

What is the formula for the damping ratio ζ of an RLC series circuit?

Accepted Answer

The damping ratio is ζ = R / (2√(L/C)). When ζ < 1, the circuit is underdamped (oscillatory response); ζ = 1 gives critically damped (fastest non-oscillatory response); ζ > 1 gives overdamped (slow non-oscillatory response). The natural angular frequency is ω₀ = 1/√(LC) rad/s, and the damped natural frequency is ωd = ω₀√(1 − ζ²).

Question 3

What is the difference between the RL and RC circuit time constants?

Accepted Answer

The RL circuit time constant is τ = L/R (seconds), and the current rises as I(t) = (V₀/R)(1 − e^(−t/τ)). The RC circuit time constant is τ = RC, governing voltage charging. For example, with L = 10 mH and R = 100 Ω, τ = 0.1 ms. The inductor's back-EMF delays current buildup in an RL circuit.

Question 4

How do you find the cutoff frequency of an RC low-pass filter?

Accepted Answer

The cutoff frequency of an RC low-pass filter is fc = 1/(2πRC) Hz. At this frequency the amplitude drops by −3 dB (to 1/√2 of its DC value). For example, with R = 10 kΩ and C = 1 μF, fc = 1/(2π × 10000 × 10⁻⁶) ≈ 15.9 Hz. Above this frequency the Bode plot rolls off at −20 dB/decade.

RC/RL Circuit Transient Response Analyzer

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