In an RC integrator, if the RC time constant is increased while the input pulse width remains the same, how do charge and discharge behaviors change during and between pulses?

Introduction / Context:
RC integrators rely on a proper relationship between the RC time constant and the pulse width of the input signal. This question examines how increasing the time constant affects the capacitor's charge and discharge behavior.

Given Data / Assumptions:

• An RC integrator receiving repetitive pulses of fixed width and amplitude.
• The RC time constant tau = R * C is increased (by raising R, C, or both).
• Pulse width and repetition period remain unchanged.

Concept / Approach:
For a fixed pulse width T_p, the fraction of full charge achieved during a single pulse is 1 - exp(-T_p / tau). As tau increases, T_p / tau decreases, thus the term 1 - exp(-T_p / tau) becomes smaller, meaning the capacitor charges less during the pulse. Similarly, between pulses, discharge follows exp(-T_gap / tau). Larger tau produces a slower discharge (i.e., discharges less between pulses).

Step-by-Step Solution:

Verification / Alternative check:
Numerical example: For T_p = 1 ms, tau = 1 ms gives charge fraction ≈ 1 - e^-1 ≈ 0.632. If tau = 5 ms, charge fraction ≈ 1 - e^-0.2 ≈ 0.181 (much less). The discharge fraction over a fixed gap also becomes slower with larger tau, confirming less discharge.

Why Other Options Are Wrong:

• Charges more / discharges more: Opposite of the exponential behavior when tau is increased.
• Charges more / discharges less: Only half correct; the charge part is wrong.
• Charges less / discharges more: Discharge statement is incorrect for larger tau.

Common Pitfalls:

• Confusing the effects of increasing tau with increasing pulse width.
• Assuming symmetrical effects without considering exponential time constants.

Final Answer:
The capacitor charges less during a pulse and discharges less between pulses