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

Answer 1

`(50)/(\pi )`Hz

Step-by-step 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 =
`(50)/(\pi )`Hz

Therefore, the frequency of the voltage is
`(50)/(\pi )`Hz