alleryStart learning →The angular frequency $\omega$ (rad/s) relates to the frequency $f$ (Hz) as
A$\omega = f$
B$\omega = 2\pi f$
C$\omega = f / (2\pi)$
D$\omega = f^2$
Answer & Solution
Correct answer: B. $\omega = 2\pi f$
1. $\omega = 2\pi f$.
2. INTUITION: one full cycle is $2\pi$ radians; $f$ cycles per second × $2\pi$ rad/cycle = $\omega$ rad/s.
3. Example: 50 Hz mains: $\omega = 2\pi(50) \approx 314\,\text{rad/s}$.
4. 60 Hz mains: $\omega \approx 377\,\text{rad/s}$.
5. Options A, C, D give wrong relationships.
_Source: Tony Kuphaldt, "Lessons in Electric Circuits — AC", Vol II, Ch 1 (Frequency)._
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