While discharging, what happens to the voltage in the capacitive circuit?

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Examoogle · Accepted Answer

Decreases exponentially

Explanation: When a charged capacitor is connected to a resistor in a closed circuit, it discharges through the resistor. The voltage across the capacitor decreases exponentially over time as the stored energy is dissipated in the form of heat.

Working Principle: During discharge, the capacitor acts as a source of current. The rate of discharge is proportional to the current flow, which in turn is proportional to the instantaneous voltage according to Ohm's Law ($I = V/R$). This leads to a first-order differential equation $dV/dt = -V/(RC)$, the solution of which is a negative exponential function.

Key Formulas: $V(t) = V_0 e^{-\frac{t}{RC}}$ — The instantaneous voltage across the capacitor at time $t$ during discharge.; $	au = RC$ — The time constant, which determines the rate of decay.

Key Points: The discharge rate is governed by the time constant $	au = RC$.; In one time constant ($	au$), the voltage drops to approximately 36.8% of its initial value.; The capacitor is considered 'fully discharged' after approximately 5 time constants.; The exponential nature arises because as voltage drops, current also drops, slowing the discharge process.

Advantages: Predictable decay based on component values.; Used in timing circuits and pulse generation.

Disadvantages: Never reaches absolute zero in theoretical time.; Sensitive to leakage resistance.

Applications: Timing circuits (e.g., 555 timers).; Filtering circuits in power supplies.; Debouncing switches.

Additional Info: The term 'exponentially' describes a process where the rate of change is proportional to the current value.. Option A and B are incorrect because the discharge process is non-linear.. Option D is incorrect because increase occurs during the charging phase, not discharging.

Answer: C is correct — The voltage across a discharging capacitor follows an exponential decay curve governed by the time constant $	au = RC$.

Exam Tip: Always remember that in RC circuits, charging and discharging are exponential processes, whereas in RL circuits, current behavior follows a similar exponential pattern.

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