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madam [21]
3 years ago
10

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
Physics
1 answer:
stealth61 [152]3 years ago
7 0

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.

<u><em>Now,</em></u>

From the question,

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

<em><u>By comparing equations (i) and (ii) the following holds;</u></em>

V = 230

ω = 100

Ф = 0

<em><u>But;</u></em>

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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