Question

In Alternating Current (A.C.) system, we generate sine wave form because

• A. It can be drawn easily
• B. It produces least disturbance in electrical circuits
• C. It is nature's standard
• D. Other waves cannot be produced easily

Hint:

Why Sinusoidal AC? Sinusoids generate LEAST DISTURBANCE IN ELECTRICAL CIRCUITS because derivatives/integrals preserve the wave shape with zero higher harmonic interference.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Harmonic analysis and mathematical properties of sinusoidal AC waveforms: a pure sine wave is the only periodic waveform whose mathematical derivative and integral remain identical in shape, producing zero higher-order harmonic distortion, minimal eddy current/hysteresis losses, and least electromagnetic interference in electrical transmission circuits.
Key Formula or Approach:
\[ \frac{d}{dt}\sin(\omega t) = \omega \cos(\omega t) = \omega \sin\left(\omega t + \frac{\pi}{2}\right) \quad \implies \quad \mathbf{Zero \text{ } Higher \text{ } Harmonics \implies Least \text{ } Circuit \text{ } Disturbance} \]

Step 2: Detailed Explanation:
In electrical power generation and AC transmission engineering:
- Alternating current power generators (alternators) standardly generate pure sinusoidal voltage waveforms ($v(t) = V_m \sin(\omega t)$):
1. Mathematical Uniqueness: The sine wave is the unique periodic mathematical function whose rate of change (derivative) and accumulation (integral) retain the exact same sinusoidal waveform (shifted in phase by $90^\circ$).
2. Least Disturbance in Electrical Circuits (B):
- Non-sinusoidal waveforms (square, triangular, sawtooth) contain infinite series of higher-order odd harmonics by Fourier analysis.
- These harmonics generate severe parasitic eddy current heating, hysteresis iron losses in transformers/motors, resonance overvoltages, and destructive electromagnetic interference (noise) in telecommunication and dairy automation control circuits.
- A pure sinusoidal wave contains only the fundamental frequency ($50\text{ Hz}$), producing the least disturbance in electrical circuits.

Step 3: Final Answer:
Therefore, sine wave is generated because It produces least disturbance in electrical circuits, corresponding to option (B).