Power-on reset (RC network): In an automatic reset circuit for a flip-flop, approximately how long does it take an RC network to charge essentially to its final value?

Introduction / Context:
Power-on reset circuits commonly use an RC network to generate a brief reset pulse as the supply ramps. Understanding exponential charging helps estimate how long the reset signal will take to deassert when the capacitor reaches near its final voltage.

Given Data / Assumptions:

• Simple first-order RC charging.
• Capacitor voltage follows V(t) = Vfinal * (1 − e^(−t/RC)).
• “Essentially charged” means within about 1% of final value in practical design.

Concept / Approach:
Rule of thumb: after 5*RC, the capacitor reaches about 99.3% of Vfinal. This is sufficient for most digital thresholds to declare the reset expired and allow normal operation.

Step-by-Step Solution:
At t = 1 RC → ~63% charged; too low for many thresholds.At t = 2 RC → ~86.5% charged; still not close to final.At t = 5 RC → ~99.3% charged; generally considered “fully charged.”

Verification / Alternative check:
Compute Verror = e^(−t/RC). For t = 5 RC, Verror ≈ 0.0067; small enough to treat as fully charged in most digital contexts.

Why Other Options Are Wrong:
1 or 2 RC leave significant residual error; 10 RC is more than needed in typical designs.

Common Pitfalls:
Ignoring tolerance of R and C and temperature drift; engineers should design reset margins accordingly.

Final Answer:
5 time constants (RC)