Correct Answer

Concept & PrincipleElectricalBasic Electrical

Option D

$360°$

Quick Summary: In rotational mechanics and electrical vector analysis, one complete revolution of a vector around a fixed point corresponds to a change in angular position of $2\pi$ radians, which is equivalent to 360 degrees. This rotation marks one full cycle of an alternating quantity (such as voltage or current) in a time-domain representation.

💡 Explanation

In rotational mechanics and electrical vector analysis, one complete revolution of a vector around a fixed point corresponds to a change in angular position of $2\pi$ radians, which is equivalent to 360 degrees. This rotation marks one full cycle of an alternating quantity (such as voltage or current) in a time-domain representation.

🔢 Key Formulas

$\theta = \omega t$ — Angular displacement formula

$\theta_{total} = 2\pi \text{ radians} = 360°$ — Rotation for one full cycle

⚙️ Working Principle

A vector (or phasor) rotating at a constant angular velocity $\omega$ (measured in radians per second) completes one full revolution relative to its starting position when the time elapsed $t$ equals the time period $T$ . Given the angular displacement $\theta = \omega t$ and $\omega = \frac{2\pi}{T}$ , substituting $t=T$ yields $\theta = 2\pi$ radians, which converts to $360°$ in circular geometry.

📌 Key Points

▸
A full circle is divided into 360 equal angular parts called degrees.
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In A.C. circuits, one complete wave cycle (positive and negative half-cycles) represents $360°$ electrical.
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Phasors rotate counter-clockwise by convention in standard engineering practice.

✅ Advantages

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Simplifies analysis of sinusoidal A.C. circuits
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Allows usage of complex numbers to represent phase differences

❌ Disadvantages / Limitations

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Assumes perfect sinusoidal waveforms
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Not directly applicable to complex non-periodic signals without Fourier decomposition

🛠️ Applications / Uses

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A.C. motor speed analysis
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Power system stability studies
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Phasor diagrams in signal processing

📄 Additional Information

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In radians, one full rotation is $2\pi$ radians.
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Option B ( $90°$ ) represents a quarter rotation (a quadrature phase shift).
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Option C ( $180°$ ) represents a half rotation, often seen as phase inversion.

📊 Diagram / Illustration

✅

D is correct — One complete rotation of a vector signifies a full cycle of $360°$ .

Core Concepts Used

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Angular Displacement Phasor Rotation A.C. Waveform Cycle

💡 EXAM TIP

Remember that $180°$ is $\pi$ radians; always verify if your calculator or formula is in degrees or radians before proceeding with phasor calculations.

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