RC charging calculation for a series R–C connected to a DC source Given: R = 22 kΩ, C = 0.02 µF, supply = 5 V. Find the time for the capacitor voltage to reach 3.4 V.

Introduction / Context:
Monostable, astable, and timing circuits frequently rely on the exponential charge of a capacitor through a resistor. This question tests understanding of the RC time constant and the natural response equation for capacitor charging toward a DC supply.

Given Data / Assumptions:

• R = 22 kΩ (22,000 Ω)
• C = 0.02 µF (20 × 10^-9 F)
• Supply voltage Vs = 5 V
• Target capacitor voltage Vc = 3.4 V
• Initial capacitor voltage assumed 0 V

Concept / Approach:

The capacitor charging law is: Vc(t) = Vs * (1 - e^(-t/(RC))). Rearranging for time gives t = -RC * ln(1 - Vc/Vs).

Step-by-Step Solution:

Verification / Alternative check:

For a quick sense check, at 1τ the capacitor reaches about 63.2% of the final value; here the target is 68%, slightly above 1τ. So the expected time is slightly more than 0.44 ms, which matches 0.501 ms.

Why Other Options Are Wrong:

0.44 ms: equals exactly τ, but the target fraction (68%) exceeds 63.2% at 1τ, so more time is needed.
0.66 ms and 0.70 ms: both overestimate because they correspond to significantly beyond 68% toward the final value.

Common Pitfalls:

Confusing 1τ with the final value; misusing degrees vs radians (not applicable here); forgetting to convert microfarads to farads; rounding errors in ln(0.32).

Final Answer:

0.501 ms