Time constant calculation: A 220 Ω resistor is in series with a 2.2 µF capacitor. Compute the RC time constant and choose the closest option.

Introduction / Context:The RC time constant quantifies how quickly voltages across a resistor-capacitor network rise or fall during charging or discharging. It is essential for timing circuits and filters.

Given Data / Assumptions:

• R = 220 Ω.
• C = 2.2 µF.
• Series RC network; ideal components.

Concept / Approach:The time constant is tau = R * C. Use SI units: ohms for resistance and farads for capacitance. Convert microfarads to farads before multiplying.

Step-by-Step Solution:C = 2.2 µF = 2.2 * 10^-6 Ftau = R * C = 220 * 2.2 * 10^-6tau = 484 * 10^-6 s = 484 µsClosest listed value: 480 µs

Verification / Alternative check:Order-of-magnitude check: 200 Ω * 2 µF ≈ 400 µs, so 220 Ω * 2.2 µF should be slightly higher, about 480 µs. This corroborates the calculation.

Why Other Options Are Wrong:

• 48 µs and 24 µs: Too small by factors of about 10 and 20.
• 2.42 µs: Off by two orders of magnitude due to unit or decimal error.

Common Pitfalls:Forgetting to convert µF to F or misplacing the decimal is the most common source of error. Also, do not confuse milliseconds with microseconds.

Final Answer:480 µs