Question

A generator produces a voltage that is given by V = 240 sin 120 t , where t is in seconds. The frequency and r.m.s. voltage are(a) 60 Hz and 240 V(b) 19 Hz and 120 V(c) 19 Hz and 170 V(d) 754 Hz and 70 V

Answer 1

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c. 19 Hz n 170 V

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Answer 2

The frequency and r.m.s. voltage are 19.09 Hz and 170 V respectively.

Explanation:

Given that,

A generator produces a voltage that is given by :

$V=240\ sin(120\ t)$

The general equation of voltage is given by :

$V=V_o\ sin(\omega t)$

On comparing above two equations,

The rms voltage is given by :

$V_{rms}=\dfrac{V_o}{\sqrt{2} }$

$V_{rms}=\dfrac{240}{\sqrt{2} }$

$V_{rms}=169.70\ V$

or

$V_{rms}=170\ V$

Angular frequency is given by :

$\omega=2\pi f$

$120=2\pi f$

f = 19.09 Hz

So, the frequency and r.m.s. voltage are 19.09 Hz and 170 V respectively.

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Topic : Alternating voltage

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