RC integrator capacitor voltage — how it changes: “The voltage across the capacitor in an RC integrator cannot change exponentially; it can change only instantaneously.” Judge this statement.

Introduction / Context:Capacitor behavior in first-order RC networks is a cornerstone of electronics. A common misunderstanding is that capacitor voltage can jump instantly. In reality, the defining property of a capacitor is that current is proportional to the rate of change of voltage, which leads to an exponential change in voltage for step inputs—not an instantaneous jump—when driven through a resistor.

Given Data / Assumptions:

• RC integrator topology with capacitor connected to ground and driven through a resistor.
• Ideal components for the conceptual model.
• Input waveforms include steps and pulses.

Concept / Approach:In an RC network, i_C = C * dv_C/dt. For a finite series resistance, dv_C/dt is finite for finite current; therefore, v_C cannot change instantaneously. For a step input, the solution is v_C(t) = V_final * (1 − exp(−t/τ)) + V_initial * exp(−t/τ), which is exponential in time. Only an ideal zero-impedance source directly across a capacitor (or infinite current) could enforce an instantaneous change—neither occurs in a standard RC integrator.

Step-by-Step Solution:

Verification / Alternative check:Oscilloscope measurements of an RC charge curve show the well-known exponential approach to a new level, reaching ~63% in 1τ, ~86% in 2τ, ~95% in 3τ, ~98% in 4τ, and ~99% in 5τ. None of these represent an instantaneous jump.

Why Other Options Are Wrong:

• Correct: Opposite of the physical behavior in an RC network.
• Valid only for ideal zero-ESR capacitors / very high frequency: ESR or frequency does not permit instantaneous voltage steps without infinite current.

Common Pitfalls:Confusing an observed fast but finite rise with an instantaneous jump; ignoring series resistance or source limitations that necessarily enforce exponential transitions.

Final Answer:Incorrect.