In an RC series circuit, when the switch is closed and the circuit is complete, what is the response

Question

In an RC series circuit, when the switch is closed and the circuit is complete, what is the response?

Examoogle · Accepted Answer

Decays with time

Explanation: In a series RC circuit connected to a DC source, the current response is a transient phenomenon that decays exponentially from its initial maximum value to zero as the capacitor charges. The capacitor behaves as a short circuit initially and an open circuit once fully charged, leading to the decay of the charging current.

Working Principle: Upon closing the switch at $t=0$, the voltage across the uncharged capacitor is zero, resulting in a maximum charging current $I_0 = \frac{V_S}{R}$. As the capacitor stores energy in its electric field, its voltage $v_C(t)$ increases, opposing the source voltage. Consequently, the net voltage across the resistor decreases over time, causing the current $i(t) = \frac{V_S - v_C(t)}{R}$ to decay towards zero following the time constant $	au = RC$.

Key Formulas: $i(t) = \frac{V_S}{R} e^{-\frac{t}{RC}}$ — Charging current equation; $	au = RC$ — Time constant of the RC circuit

Key Points: The capacitor acts as a short circuit at $t = 0^+$.; The capacitor acts as an open circuit at $t = \infty$.; The transient period is theoretically infinite but practically considered complete after $5	au$.; Energy is dissipated in the resistor during the charging process.

Advantages: Provides predictable time-based control; Essential for filter and timing applications

Disadvantages: Energy loss as heat in the resistor; Voltage-dependent charging time

Applications: Timing circuits; Signal filtering and smoothing; Debouncing switches

Additional Info: The term 'response' in this context refers to the transient current flowing through the circuit loop.. Option A is incorrect as the current varies due to charging. Option C describes the capacitor voltage, not the current. Option D describes an oscillatory circuit (RLC), not RC.

Answer: B is correct — The charging current in an RC series circuit decays exponentially with time as the capacitor potential increases to oppose the source voltage.

Exam Tip: Always remember that in series RC circuits, the voltage across the capacitor grows exponentially while the current decays; for RL circuits, the roles are reversed regarding inductor current vs. voltage.

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