Capacitors charge and discharge in __________ manner.

Question

Examoogle · Accepted Answer

Exponential

Explanation: Capacitors in a DC circuit with resistance exhibit an exponential charging and discharging behavior governed by the time constant $	au = RC$. The voltage across the capacitor does not change instantaneously but follows a natural logarithmic decay or growth curve as charge accumulates or dissipates.

Working Principle: During charging, the rate of charge flow is proportional to the difference between the supply voltage and the capacitor voltage. As the capacitor charges, this voltage difference decreases, causing the charging current to decrease exponentially until the capacitor is fully charged. During discharging, the stored energy is released through the circuit resistance, leading to an exponential decay of both voltage and current.

Key Formulas: $V_c(t) = V_s(1 - e^{-\frac{t}{RC}})$ — Charging voltage expression; $V_c(t) = V_0e^{-\frac{t}{RC}}$ — Discharging voltage expression; $	au = RC$ — Time constant of the circuit

Key Points: The transient response of a capacitor is always exponential in a resistive circuit.; One time constant ($	au$) corresponds to approximately 63.2% of the total voltage change during charging.; The circuit reaches steady state after approximately $5	au$.; Capacitors act as an open circuit to steady-state DC.

Advantages: Predictable transient behavior; Essential for timing and oscillator circuits

Disadvantages: Non-linear rate of change makes precise control difficult without feedback; Energy storage is limited by dielectric strength

Applications: Timing circuits (555 timers); Smoothing filters in power supplies; Signal coupling and decoupling

Additional Info: In a purely capacitive circuit without resistance, the charging time would be zero (impulse current), which is physically impossible as it would require infinite power.. Option A is incorrect because linear behavior is only found in purely resistive networks or ideal current sources.

Answer: D is correct — The voltage across a charging or discharging capacitor follows an exponential curve defined by the RC time constant.

Exam Tip: Always remember that $5	au$ is the standard threshold for considering a capacitor fully charged or discharged in engineering approximations.

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