0.005 s to go from zero to 90 degrees; frequency?

0.005 s to go from zero to 90 degrees; frequency?

• A. 20 Hz
• B. 50 Hz
• C. 2 Hz
• D. 5 Hz

Answer: (B)

The concept being tested is how phase, time, and frequency relate in an AC waveform. A change of 90 degrees is one quarter of a full cycle, so the time to reach 90 degrees is a quarter of the period: t = T/4. If that quarter-cycle takes 0.005 s, the full period is T = 4 × 0.005 = 0.02 s, which gives a frequency f = 1/T = 1/0.02 = 50 Hz. The other frequencies would require different quarter-cycle times: 20 Hz would be a quarter-cycle of 0.0125 s, 2 Hz would be 0.125 s, and 5 Hz would be 0.05 s, none of which match 0.005 s.

The concept being tested is how phase, time, and frequency relate in an AC waveform. A change of 90 degrees is one quarter of a full cycle, so the time to reach 90 degrees is a quarter of the period: t = T/4. If that quarter-cycle takes 0.005 s, the full period is T = 4 × 0.005 = 0.02 s, which gives a frequency f = 1/T = 1/0.02 = 50 Hz. The other frequencies would require different quarter-cycle times: 20 Hz would be a quarter-cycle of 0.0125 s, 2 Hz would be 0.125 s, and 5 Hz would be 0.05 s, none of which match 0.005 s.