RC Transient Rule of Thumb Evaluate the statement: “Five time constants are required for a capacitor to charge fully or discharge fully.”

Introduction / Context:
The time response of RC circuits is exponential. Engineers often use “time constants” to estimate how quickly a capacitor approaches its final value. This item checks whether you understand the difference between “practically complete” and “mathematically complete.”

Given Data / Assumptions:

• First-order RC circuit with time constant tau = R * C.
• Step excitation for charge or discharge.
• Ideal components for the basic exponential model.

Concept / Approach:

The voltage or current follows an exponential of the form 1 − exp(−t/tau) (charging) or exp(−t/tau) (discharging). Exponentials asymptotically approach their final value and never reach it in finite time. The “5 * tau” guideline means “within about 1% of final,” not “fully.”

Step-by-Step Solution:

Verification / Alternative check:

Compute residual error after 5 * tau: exp(−5) ≈ 0.0067. That is less than 1%, which most practical designs treat as “effectively settled.” But “fully” would imply 100%, which requires infinite time for an exponential approach.

Why Other Options Are Wrong:

“True” and conditional versions misinterpret the engineering rule of thumb as a strict equality. The “1% rule” is practical, not absolute; device type or source resistance does not change the asymptotic nature.

Common Pitfalls:

Assuming a process is complete after a fixed number of time constants, and forgetting that measurement tolerances and application needs dictate what “settled” means (e.g., 0.1%, 1%, 5%).

Final Answer:

False