Charging behavior of an RC network — which statements are true as a capacitor charges from a DC source? Assume a simple series R–C connected to a constant DC supply and select the best overall answer.

Introduction / Context:Classic RC charging exhibits exponential behavior for both capacitor voltage and loop current. The time constant tau = R * C sets the rate. After about 5 * tau, the capacitor is essentially fully charged for practical purposes. This question checks fundamental time-constant intuition.

Given Data / Assumptions:

• Series R–C driven by an ideal DC source
• Initial capacitor voltage is zero
• No leakage and constant R

Concept / Approach:Standard equations for charging are: Vc(t) = V_s * (1 − e^(−t/tau)) and I(t) = (V_s/R) * e^(−t/tau). Engineers often use 5 * tau as the practical "full-charge" time where Vc ≈ 99%.

Step-by-Step Solution:

Verification / Alternative check:Plotting Vc(t) and I(t) vs time confirms the exponential rise and decay and the 5 * tau rule of thumb.

Why Other Options Are Wrong:

• Options a, b, c are all correct statements; thus "all of the above" is the best choice.
• "None of the above" contradicts established RC theory.

Common Pitfalls:

• Assuming charging is linear; it is exponential.
• Equating 5 * tau with an exact limit; it is a practical guideline.

Final Answer:all of the above