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:
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:
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:
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.
Discussion & Comments