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Circuit and electromagnetism basics

What is the frequency of a sinusoidal AC voltage whose instantaneous value is v = 10 sin(100πt) [V]? (t in seconds)

  1. AAbout 314 Hz
  2. B50 Hz
  3. C100 Hz
Show answer and explanation

Answer: B. 50 Hz

In a sine wave v = Vm sin(ωt), ω is the angular frequency, related to the frequency f by ω = 2πf. Here ω = 100π rad/s, so f = 100π/(2π) = 50 Hz and the period is 1/50 = 20 ms. The peak is 10 V and the RMS value is 10/√2 ≈ 7.07 V. Take care not to confuse angular frequency (rad/s) with frequency (Hz).

  • A. About 314 Hz mistakes the angular frequency ω = 100π ≈ 314 rad/s for the frequency.
  • B. Correct. f = ω/(2π) = 50 Hz.
  • C. 100 Hz divides ω by π only and forgets the factor of 2.
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