Repair for missing schematic — “If the pulse width were cut in half in the given RC pulse circuit, the voltage across the resistor at the end of the pulse would be ______.” Without R, C, τ, and the original pulse width, can a unique numeric value be selected?

Difficulty: Easy

Correct Answer: Cannot be determined from the information provided

Explanation:


Introduction / Context:
For an RC network excited by a pulse, the voltage across the resistor at the end of the pulse depends on the exponential evolution during the on-time. That evolution is set by the time constant τ = R * C and the actual on-time (pulse width). Halving the pulse width changes the settling time, but without the numeric τ and original timing, the final value cannot be pinned down to a single number.


Given Data / Assumptions:

  • No values for R, C, or τ are provided.
  • No explicit pulse amplitude or original pulse width is given.
  • Output node location is not fully specified in the missing figure.


Concept / Approach:
The resistor voltage in a simple RC driven by a step is v_R(t) = V_in * exp(−t/τ) (for a series RC with output across R after a step to V_in), or the complement thereof depending on the exact topology. At t = PW (end of pulse), v_R(PW) depends on exp(−PW/τ). If PW is halved, the new value depends on exp(−(PW/2)/τ). Without τ and PW, the numeric outcome is undetermined.


Step-by-Step Solution:

State general form: v_end ∝ exp(−PW/τ) (topology dependent scale).Halve PW → v_end,new depends on exp(−(PW/2)/τ).No τ or PW given → cannot compute a numeric result.Therefore, a single numeric choice is not justifiable.


Verification / Alternative check:
Try two examples: If PW = 5τ, exp(−PW/τ) ≈ 0.007; if PW = 0.5τ, exp(−PW/τ) ≈ 0.607. The outcomes are vastly different, proving dependence on missing data.


Why Other Options Are Wrong:

  • 0 V / equals source / fixed fractions: these assert specific conditions that may or may not hold; they require τ and PW.
  • “One-half of the original”: exponential processes do not in general scale linearly with time halving.


Common Pitfalls:
Assuming a universal “0.37” or “0.5” result; those come from particular τ:PW ratios, not from the act of halving itself.


Final Answer:
Cannot be determined from the information provided.

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