A sine wave has a afrequency of 50 Hz, Its angular frequency is _____________________ radian/second.
A
$100\pi$
B
$50\pi$
C
$25\pi$
D
$5\pi$

Question

A sine wave has a afrequency of 50 Hz, Its angular frequency is _____________________ radian/second.

Examoogle · Accepted Answer

$100\pi$

Explanation: Given: Frequency f = 50 Hz

Formula Used: $$\omega = 2\pi f$$

Steps: Identify the relationship: The relationship between angular frequency ($\omega$) in radians per second and frequency ($f$) in Hertz is given by the standard formula.. Substitute the values: Substitute the given frequency $f = 50$ Hz into the formula.. Calculate the result: Perform the multiplication to find the angular frequency.

Answer: A is correct because substituting the frequency $f = 50$ Hz into the formula $\omega = 2\pi f$ yields $\omega = 100\pi$ rad/s.

Exam Tip: This relationship is fundamental in Electrical Engineering for converting between cycles per second and radial movement, which is essential when calculating capacitive ($X_C = \frac{1}{2\pi f C}$) and inductive ($X_L = 2\pi f L$) reactance.

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