Question

the relation between an A.C. voltage source and time in SI units is V=120 sin(100×3.14t)cos(100×3.14t) volt value of peak voltage and frequency will be respectively

Answer 1

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Answer 2

Answer:

Peak voltage = 60 volt

Frequency = 100 Hz

Explanation:

As per the question,

Given voltage source

V = 120 sin(100 × 3.14t) cos(100 × 3.14t)

   = 60 × 2 sin(100 × 3.14t) cos(100 × 3.14t)

Since,

2 sinA cosA = sin2A

Therefore,

  V = 60 sin(200 × 3.14t)

  V = 60 sin(628t)

As we know that, the general equation of voltage source is represented by:

V = V₀ sin(ωt)

Where,

V₀  = peak voltage

ω = 2π f,      f = frequency

Now,

On comparing the given voltage source with general form, we get

V₀ = 60 volt

And

ω = 628 = 2π f

⇒ f = 100 Hz

Hence,  the value of peak voltage and frequency is 60 volt and 100 Hz respectively.