RC charging time constant: in a standard first-order RC charging circuit, the time to reach practical full charge is approximately which multiple of RC?

Introduction / Context:
The time constant τ = R * C sets the speed of exponential charging in RC networks. Engineers often use a practical benchmark for “full” charge to estimate delays, settling times, and sampling windows in analog systems.

Given Data / Assumptions:

• Standard RC charging from a DC source through a resistor.
• No significant leakage or series resistance beyond R.
• “Full charge” means about 99% of final value (common engineering convention).

Concept / Approach:
Capacitor voltage during charging is Vc(t) = Vs * (1 - e^(-t/RC)). At t = 5RC, e^(-5) ≈ 0.0067, so Vc ≈ 99.33% of Vs. This is widely accepted as the time to essentially reach the final value for practical purposes.

Step-by-Step Solution:

Verification / Alternative check:
At 4RC, Vc ≈ 98.2% Vs; at 6RC, ≈ 99.75% Vs. Many references standardize on 5RC as a convenient “practical full charge.”

Why Other Options Are Wrong:

• RC: Only ~63.2% charged.
• 6 RC: Also near full, but the conventional benchmark used in design notes is 5RC.
• None of the above: Incorrect because 5RC is the conventional answer.

Common Pitfalls:

• Confusing time constant (63.2%) with practical full charge (~99%).
• Assuming exact “100%” is achievable in finite time; exponential never truly reaches it.

Final Answer:
5 RC