Alternating Current In Europe, the voltage of the alternating current coming through an electrical outlet can be modeled by the function V 2

Question

Alternating Current In Europe, the voltage of the alternating current coming through an electrical outlet can be modeled by the function V 230 sin (100t), where tis measured in seconds and Vin volts.What is the frequency of the voltage

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Farah 3 years 2021-08-17T09:27:09+00:00 1 Answers 13 views 0

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  1. Adela
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    2021-08-17T09:28:53+00:00
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    Answer:

    \frac{50}{\pi }Hz

    Explanation:

    In alternating current (AC) circuits, voltage (V) oscillates in a sine wave pattern and has a general equation as a function of time (t) as follows;

    V(t) = V sin (ωt + Ф)            —————–(i)

    Where;

    V = amplitude value of the voltage

    ω = angular frequency = 2 π f        [f = cyclic frequency or simply, frequency]

    Ф = phase difference between voltage and current.

    Now,

    From the question,

    V(t) = 230 sin (100t)              —————(ii)

    By comparing equations (i) and (ii) the following holds;

    V = 230

    ω = 100

    Ф = 0

    But;

    ω = 2 π f = 100

    2 π f = 100             [divide both sides by 2]

    π f = 50

    f = \frac{50}{\pi }Hz

    Therefore, the frequency of the voltage is \frac{50}{\pi }Hz

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