Mains frequency comparison: What is the difference in waveform period between 60 Hz utility power and 50 Hz utility power (express your choice by the closest value)?

Introduction:Time-domain understanding of mains frequency is crucial for power conversion, timing references, and alias-free sampling. The period T is the reciprocal of frequency f, so small frequency differences translate into concrete milliseconds per cycle differences.

Given Data / Assumptions:

• f1 = 60 Hz (common in North America and parts of Asia).
• f2 = 50 Hz (common in Europe and many other regions).
• We want ΔT = |T60 − T50|.

Concept / Approach:Compute T from T = 1 / f. For 60 Hz, T60 ≈ 0.01667 s = 16.67 ms. For 50 Hz, T50 = 0.020 s = 20.00 ms. The absolute difference is about 3.33 ms. Among the provided discrete choices, 3 ms is the closest approximation (rounding to the nearest millisecond).

Step-by-Step Solution:

Verification / Alternative check:Express ΔT precisely as 1/50 − 1/60 = (60 − 50) / (3000) s = 10/3000 s = 1/300 s ≈ 3.333 ms; rounding confirms the selected option.

Why Other Options Are Wrong:

• 16 ms or 20 ms: These are full periods, not the difference.
• 4 ms: Farther from the exact 3.33 ms than 3 ms.

Common Pitfalls:Mixing up frequency with period; forgetting to convert seconds to milliseconds; selecting a full period instead of the difference.

Final Answer:3 ms