A capacitor does not allow sudden changes in _________

Question

Examoogle · Accepted Answer

Voltage

Explanation: A capacitor is a passive electrical component that stores energy in an electric field. Because the energy stored is proportional to the square of the voltage, any instantaneous change in voltage would require an infinite current, which is physically impossible in an ideal circuit.

Working Principle: The relationship between current and voltage in a capacitor is defined by the equation $i(t) = C \frac{dv(t)}{dt}$. If the voltage $v(t)$ were to change instantaneously at a specific time $t$, the derivative $\frac{dv}{dt}$ would approach infinity, implying an impulsive current of infinite magnitude. To maintain finite energy and current, the voltage across a capacitor must remain continuous.

Key Formulas: $i(t) = C \frac{dv(t)}{dt}$ — Instantaneous current-voltage relationship for a capacitor; $v(t) = \frac{1}{C} \int_{-\infty}^{t} i(	au) d	au$ — Voltage as an integral of current over time

Key Points: Capacitors act as open circuits to steady-state DC voltage ($f=0$).; In switching transients, the capacitor voltage just after switching is equal to the voltage just before switching.; Inductors exhibit the dual property, resisting sudden changes in current ($i_L$).; The inability to change voltage instantaneously is due to the finite time required to move charge onto the plates.

Advantages: Energy storage capability in electric fields; Filtering of high-frequency noise in circuits

Disadvantages: Finite breakdown voltage limits; Leakage current in practical electrolytic capacitors

Applications: Power factor correction; Smoothing circuits in DC power supplies

Additional Info: Option A is incorrect because current in a capacitor can change instantaneously (e.g., when a step voltage is applied to a discharged capacitor).. The time constant $	au = RC$ determines the rate at which voltage changes in a circuit containing resistance and capacitance.

Answer: B is correct — A capacitor does not allow sudden changes in voltage because that would require an infinite current flow.

Exam Tip: Always remember the mnemonic 'CIVIL': for Capacitor, Current leads Voltage (CIV); for Inductor, Voltage leads Current (LIL/VIL).

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