Question

If an alternating voltage is given by V=100sin(314t) then calculate rms value of voltage, frequency of emf and time period.

Answer 1

$V_{rms}=141.42\ V$ is the rms voltage

$f=0.5\ Hz$

$T=2\ s$

Explanation:

Here we are given that:

$V=100\ \sin(314\ t)$

here:

$V_0=100\ V$ is the maximum value of the voltage.

For a sinusoidal parameter we have the RMS value as:

$V_{rms}=\frac{V_0}{\sqrt{2} }$

Hence

$V_{rms}=\frac{100}{\sqrt{2} }$

$V_{rms}=141.42\ V$

On Comparing  we've:

$\omega=314\ rad.s^{-1}$

we know :

$\omega=2\pi.f$

where:

$f=$ frequency

$f=\frac{314}{2\pi}$

$f=0.5\ Hz$

Time period:

$T=\frac{1}{f}$

$T=2\ s$

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TOPIC: wave equation

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