Repair for missing values — “If the pulse source has an internal resistance of 80 Ω in the given circuit, it will take ______ for the output voltage to decrease to zero.” Can a time-to-zero be specified for a first-order RC without knowing C (and topology)?

Introduction / Context:
First-order RC voltages decay exponentially and never reach absolute zero in finite time; designers use practical thresholds (e.g., 1τ ≈ 63% settled, 5τ ≈ 99% settled). The question as written lacks the capacitance and full topology, yet asks for a specific time “to zero,” which is not physically precise and cannot be computed numerically without τ.

Given Data / Assumptions:

• Only the source resistance Rs = 80 Ω is mentioned.
• Capacitance C and any additional series/parallel resistances are unknown.
• No threshold (e.g., to 1% or to 0.1%) is specified.

Concept / Approach:
Decay time constant is τ = R_eq * C, where R_eq is the effective resistance seen by the capacitor during discharge (often Rs plus any series elements). Without C and R_eq, τ is unknown. Moreover, an exponential strictly reaches zero only as t → ∞; practical “zero” must be defined via a percentage, such as 5τ for ≈99% decay.

Step-by-Step Solution:

Verification / Alternative check:
Pick example C values: with C = 1 µF, τ = 80 µs; with C = 10 µF, τ = 800 µs. Times differ by 10×, showing sensitivity to the missing parameter.

Why Other Options Are Wrong:

• “Exactly 5τ” or “1τ”: these are rules of thumb for percentages, not true zero.
• “Independent of C” or “equals the pulse period”: incorrect generalizations.

Common Pitfalls:
Forgetting that first-order exponentials only asymptotically reach zero; ignoring the need to specify a decay threshold.

Final Answer:
Cannot be determined from the information provided.