Which of the following depends on charging and discharging rate of a capacitor?

Question

Examoogle · Accepted Answer

Time constant

Explanation: The time constant of an RC circuit, denoted by $	au$, is the defining factor that determines the rate at which a capacitor charges or discharges. It represents the time required for the capacitor voltage to reach approximately 63.2% of its final value during charging or to fall to 36.8% of its initial value during discharging.

Working Principle: In a series RC circuit, the current flow is governed by the relation $v_c(t) = V_s(1 - e^{-t/	au})$. The parameter $	au = RC$ determines the exponential decay or growth rate of the circuit. A larger time constant results in a slower charging and discharging process, whereas a smaller time constant leads to rapid changes in voltage and current.

Key Formulas: $	au = R \cdot C$ — definition of time constant in an RC circuit; $v_c(t) = V_0(1 - e^{-t/RC})$ — charging voltage equation

Key Points: One time constant ($	au$) equals the product of resistance and capacitance.; A capacitor is considered fully charged after approximately 5 time constants ($5	au$).; The rate of change of voltage is inversely proportional to the time constant.

Advantages: Allows controlled delay in circuit response.; Essential for timing applications like oscillators and filters.

Disadvantages: Sensitivity to component tolerance (R and C variations affect $	au$).; Non-linear charging profile complicates precise instantaneous measurement.

Applications: Pulse shaping circuits; Electronic timers; Low-pass and High-pass filters

Additional Info: The unit of time constant is seconds (s) when resistance is in Ohms ($\Omega$) and capacitance in Farads (F).. Option B (Current), C (Power), and D (Voltage) are instantaneous variables that depend on the time constant, rather than defining the rate itself.

Answer: A is correct — The time constant ($	au$) is the characteristic parameter that dictates the speed of the capacitor charging and discharging process.

Exam Tip: Always remember that $5	au$ is the practical rule of thumb for when a capacitor reaches steady-state, which is a frequently tested concept in competitive exams.

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