Write the mathematical expression for a sinusoidal voltage having peak value of 200 V and frequency of 50 Hz.

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PGCIL DT Electrical 5 May 2023 Official Paper
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  1. \(\frac{200}{\sqrt2}\)sin 50 t V
  2. \(\frac{200}{\sqrt2}\)sin 100π t V
  3. 200sin 100π t V
  4. 100sin 100π t V

Answer (Detailed Solution Below)

Option 3 : 200sin 100π t V
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Concept:

F3 S.B Madhu 13.03.20 D3

The general expression for a sin wave shown above is given by:

v(t) = Vm sin ωt

Vm = Maximum or peak value of the sinusoidal wave

ω = 2πf = Frequency

Calculation:

With Vm = 200 V, and f = 50 Hz, the mathematical expression will be:

v(t) = Vm sin 2πft 

v(t) = 200 sin (2×π×50)t

v(t) = 200 sin 100πt V

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