Time-constant insight: Is it accurate to say a capacitor is fully charged in 4 time constants (4τ) in a first-order RC charging circuit?

Introduction / Context:
First-order RC charging follows an exponential approach to the final value. Because exponentials are asymptotic, the capacitor voltage gets closer and closer to the source voltage but mathematically reaches it only as time approaches infinity. Practical rules of thumb use percentages at specific multiples of the time constant τ = R * C.

Given Data / Assumptions:

• Standard step response v_C(t) = V * (1 − e^(−t/τ)).
• Definition of τ = R * C.
• Engineering tolerance for 'fully charged' is approximate, not exact.

Concept / Approach:
At t = 1τ, v_C ≈ 63%; 2τ ≈ 86%; 3τ ≈ 95%; 4τ ≈ 98%; 5τ ≈ 99.3%. Many practitioners call 5τ effectively full for practical purposes. Therefore, the claim that the capacitor is fully charged in 4τ is inaccurate; at 4τ it is close (about 98%), but not fully, and 5τ is the more common benchmark for 'essentially charged.'

Step-by-Step Solution:

Verification / Alternative check:
Oscilloscope measurements of step response match the exponential curve and common 5τ guideline used in design texts.

Why Other Options Are Wrong:

Common Pitfalls:
Equating 'nearly full' with 'fully' without specifying tolerance; ignoring that many specifications require explicit percentage thresholds.

Final Answer:
Incorrect