During the charging process of a capacitor connected to a DC source through a resistor, how does the voltage across the capacitor's terminals change with time?

Introduction:
This question tests understanding of the transient behavior of a capacitor in a simple RC charging circuit. When a DC source is applied through a resistor, the capacitor voltage evolves over time rather than changing instantaneously, due to the energy storage nature of capacitance.

Given Data / Assumptions:

• Ideal DC source applied to a series RC circuit.
• Initial capacitor voltage is 0 V (uncharged state).
• No leakage and linear, time-invariant components.

Concept / Approach:
The capacitor voltage in an RC charging circuit follows an exponential rise described by v_C(t) = V_s * (1 - exp(-t / (R * C))). It starts at 0 V and asymptotically approaches the source voltage V_s as time increases. The time constant τ = R * C sets the rate of rise.

Step-by-Step Solution:
At t = 0+, v_C = 0 V because the capacitor initially behaves like a short for AC changes.As time progresses, charge accumulates on the plates: i(t) = (V_s / R) * exp(-t / τ).The decreasing current causes a decreasing rate of voltage change across the capacitor.As t → ∞, exp(-t / τ) → 0, so v_C → V_s and the current tends to 0 A.

Verification / Alternative check:
Energy stored in the capacitor is E = 0.5 * C * V_s^2. Since energy storage builds gradually, the terminal voltage must increase monotonically toward V_s rather than drop or oscillate in an ideal RC circuit.

Why Other Options Are Wrong:

• It decreases from the source voltage to 0: This describes discharging, not charging.
• It remains constant: Contradicts transient behavior of RC circuits.
• It instantly jumps then drops: An ideal capacitor cannot change voltage instantaneously.
• It oscillates: No inductive elements are present to support oscillations.

Common Pitfalls:

• Assuming immediate voltage change across a capacitor (violates dv/dt constraints).
• Confusing charging with discharging waveforms.
• Ignoring the role of the time constant τ = R * C.

Final Answer:
It increases from 0 toward the source voltage.