What is the final current while charging a capacitor?

Question

Examoogle · Accepted Answer

Zero

Explanation: When a capacitor is connected to a DC voltage source, it charges until the voltage across its plates equals the source voltage. Once the capacitor reaches steady-state, it acts as an open circuit to DC, resulting in zero current flow.

Working Principle: The charging current follows an exponential decay governed by the time constant $	au = RC$. Initially, the capacitor acts like a short circuit because the potential difference across it is zero. As charge accumulates, the voltage across the capacitor $V_c$ increases, opposing the source voltage $V_s$, which decreases the potential difference across the resistor and consequently drops the current toward zero.

Key Formulas: $i(t) = \frac{V}{R} e^{-\frac{t}{RC}}$ — Expression for charging current at time t; $	au = RC$ — Time constant of the RC circuit

Key Points: At $t = 0$, the capacitor is uncharged and current is maximum: $I_{max} = V/R$.; At steady state ($t \approx 5	au$), the capacitor is fully charged and $I = 0$.; The capacitor blocks DC current in a steady-state condition.; The rate of charging depends on the circuit resistance and capacitance.

Advantages: Stores energy in an electric field; Acts as a DC blocking element in filters

Disadvantages: Cannot maintain current flow indefinitely in DC circuits; Finite time required for charging

Applications: Timing circuits; Filter circuits in power supplies; Energy storage systems

Additional Info: The transient period is theoretically infinite but is practically considered complete after $5$ time constants.. Option C (Infinity) is wrong because finite resistance limits the initial current to $V/R$.

Answer: B is correct — At the steady-state condition, the capacitor voltage equals the source voltage, effectively blocking the DC current path.

Exam Tip: Always remember that in DC circuits, a capacitor is an open circuit at $t = \infty$, whereas an inductor is a short circuit at $t = \infty$.

Related Questions

Discussion (0)