Final answer:
The two times in the first period following t = 0 when the instantaneous voltage in 60-Hz AC equals Vrms and -Vrms are 4.17 ms and 16.67 ms, respectively. These times correspond to the phase angles where the sine function of the AC signal is 1/√2 and -1/√2.
Step-by-step explanation:
To find the two times in the first period following t = 0 when the instantaneous voltage in 60-Hz AC equals to Vrms and -Vrms, we need to understand how AC voltage functions. A 60 Hz AC voltage signal completes one full cycle every 1/60 seconds, which is approximately 16.67 milliseconds (ms). The root mean square (RMS) value of an AC voltage is the equivalent DC voltage that delivers the same power to a load. The peak voltage (…V0) of an AC signal is related to the Vrms by the equation Vrms = V0/√2.
For a sine wave, which is the usual waveform of household AC, the times at which the sine wave is at its RMS value occur at the points where the sine function equals to 1/√2 or -1/√2. Since the frequency is 60 Hz, we can calculate the times by finding the phase angles where the sine function has these values and then converting to time using the period of the wave.
With the above considerations, we can conclude that the correct times at which the instantaneous voltage equals Vrms and -Vrms in the first period after t = 0 for a 60 Hz AC signal are 4.17 ms and 16.67 ms respectively. This corresponds to the phase angles of 45 degrees and 225 degrees. Hence the correct answer with respect to the options given is: (b) (a) 4.17 ms (b) 16.67 ms.