Correct Answer

Direct FormulaElectricalBasic Electrical

Option C

314

Quick Summary: Given: Frequency f = 50 Hz.

📋 Given

Frequency f = 50 Hz.

🔢 Formula Used

ω=2πf\omega = 2 \pi fω=2πf

🔢 Step-by-Step Solution

Identify the relationship

The angular velocity $\omega$ (measured in radians per second) is related to the frequency $f$ (measured in Hertz) of an alternating current signal by the standard formula.

ω=2πf\omega = 2 \pi fω=2πf

Substitute the values

Given that the frequency $f = 50$ Hz and using the approximation $\pi \approx 3.14159$ , substitute these into the formula.

ω=2×3.14159×50\omega = 2 \times 3.14159 \times 50ω=2×3.14159×50

Calculate the result

Perform the multiplication: $2 \times 50 = 100$ , then multiply by $\pi$ .

ω=100×3.14159=314.159≈314 rad/s\omega = 100 \times 3.14159 = 314.159 \approx 314 \text{ rad/s}ω=100×3.14159=314.159≈314 rad/s

✅

C is correct because the angular velocity is calculated as $2 \times \pi \times 50$ , which yields approximately 314 rad/s.

Core Concepts Used

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Angular Velocity A.C. Fundamentals Frequency-Angular Velocity Relationship

💡 EXAM TIP

This relationship is fundamental in power systems; remember that in India, the standard power supply frequency is 50 Hz, leading to an angular frequency of approximately 314 rad/s, which is often used in calculating inductive and capacitive reactance ( $X_L = \omega L$ and $X_C = \frac{1}{\omega C}$ ).

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