555 monostable design — find C1 for a required pulse width A 555 timer operates as a monostable (one-shot) with R1 = 1 MΩ. Determine the value of C1 required to obtain a pulse width of 2 s using t = 1.1 * R * C.

Introduction / Context:Choosing the timing capacitor for a 555 monostable is a straightforward calculation, but unit conversions must be handled carefully to avoid errors of orders of magnitude. Here we design for a 2-second pulse with a large timing resistor.

Given Data / Assumptions:

• R1 = 1 MΩ = 1,000,000 Ω.
• Desired t = 2 s.
• Formula: t = 1.1 * R * C.

Concept / Approach:Solve for C: C = t / (1.1 * R). After computing in farads, convert to microfarads to select a practical capacitor value. Consider real-world tolerances and leakage when choosing the dielectric and voltage rating.

Step-by-Step Solution:

Verification / Alternative check:Back-calculate: t ≈ 1.1 * 1 MΩ * 1.8 µF = 1.98 s, very close to 2 s, well within typical component tolerances (R ±5%, C ±10% or more). Selecting 2.0 µF yields ~2.2 s if a longer pulse is preferred.

Why Other Options Are Wrong:

• 18 F / 18 nF / 18 pF / 0.18 µF: all off by orders of magnitude compared with the required microfarad range.

Common Pitfalls:

• Confusing mega (10^6) with kilo (10^3), and micro (10^-6) with nano (10^-9).

Final Answer:1.8 µF